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Abstract Generator

Get your abstract written – skip the headache., writefull's abstract generator gives you an abstract based on your paper's content., paste in the body of your text and click 'generate abstract' . here's an example from hindawi., frequently asked questions about the abstract generator.

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What are the Abstract Generator's key features?

Free Abstract Generator

Make an abstract for your paper in 4 steps:

• Choose between a simple and an advanced option
• Paste the text or add the details
• Click “Generate”
• Check and copy the result

Your abstract may be:

• ⭐️ The Tool’s Benefits
• 🤔 Why Use Our Tool?

📝 What Is an Abstract?

• ✍️ How to Write It
• ✨ Abstract Example

🔗 References

⭐️ abstract generator: the benefits, 🤔 why use online abstract generator.

Having trouble writing an abstract? You’re not alone.

Crafting an abstract can be problematic, especially when dealing with voluminous work. After all, converting a 100-page academic paper into 150 words is not an easy task. And this is where an abstract maker can help you immensely.

The amount of time you’ll save by relying on a machine to do the work for you is huge. Not to mention the result will be entirely error-free. No logical, grammatical, or other mistakes will spoil your piece.

Sounds interesting? Then, keep reading to learn more about abstracts and our generator.

An abstract is a brief summary of a work. Usually, it's a single paragraph containing 150 to 250 words. It describes all the key points and elements of an article, essay, or work of any other format.

Keep in mind that an abstract merely describes a text. It shouldn’t be an evaluation or an attempt to defend the paper. Instead, it’s just an overview.

Structure of an Abstract

An abstract is not a simple summary. It has a specific structure and should contain the following elements:

Remember that an abstract is separate from the rest of the paper. For the reader to get the complete picture of your research, your abstract must include everything listed above.

✍️ How to Write an Abstract

It can be tempting to go and write an abstract right away. But make sure to finish the planning of your work first. You want to write your abstract about your piece's contents, not build the contents around your abstract.

To make the writing process easier, divide it into 5 manageable steps:

• Check the requirements. First off, you need to know how much you are allowed to write. An average abstract is about 150-250 words long, but there is often a strict limit. Make sure to stay within it!
• Establish the goal and the problems of the research. The reader needs to know what your paper will be about right from the get-go. That’s why you need to formulate your thesis and showcase it first.
• Establish the methods. Tell the reader how you did your research. Don’t go in too deep: simply describe the methods without unnecessary details.
• Describe the results. Write a couple of sentences about the outcome of your investigation.
• Write a conclusion. Address the issue you established in the second step. You might also want to mention your work’s limitations regarding your research samples or methods. Try to give the reader a clear understanding of your goal and how you achieved it.

Want to make the process even easier? Use our abstract tool! Online generators like ours will help you craft an excellent paragraph in a matter of seconds.

Abstract Writing Tips

Finally, we want to help you make your abstract truly amazing. Check out our best tips below:

• It's best to get to the point immediately and without adding any filler or unnecessary details.
• The less specific your abstract is, the better.
• Check out some examples before you start writing. Sometimes the best way to learn something is to watch how everyone else does it.
• Avoid long sentences or bizarre vocabulary to make an abstract paragraph as concise as possible.
• It’s a great idea to single out some keywords from your outline and put them into your abstract.
• Don't forget about formatting. Any serious academic work has its requirements. Make sure you check them before writing your piece.

Following these simple tips will make you a master of abstract writing.

✨ Free Abstract Sample

As an example, check out this abstract of the article “Bioeffcacy of Mentha piperita essential oil against dengue fever mosquito” by Sarita Kumar:

The Mentha balsamea, or peppermint plant, is a result of cross-breeding between spearmint and water mint. These plants are most commonly used in the area of repelling insects. The following research revolves around peppermint oil insect repellent and its development. As a part of an experiment, we obtained 25 grams of fresh peppermint and, after grinding it, put it in a glass jar with olive oil. The jar was then left for two days in a warm temperate. Next, the oil was strained with a cheesecloth, gathered, and diluted at 70%. It then got separated into three different spray bottles. The test was to put the spray sample into a jar with mosquitoes and equate the result to the same test with a commercial repellant. Thus, we challenged the stereotype of synthetic repellents being more efficient than their analogs made from natural materials.

That will be the end of our guide on abstract writing. Thank you for reading, and make sure to try out our abstract writer tool to get the best results!

❓ Abstract Generator FAQ

❓ how do you write an abstract for a research paper.

You may use an abstract tool and make the writing process entirely automatic. If you can’t use it, write an abstract yourself by describing the following:

• The main problem.
• Background information.
• The end goal.
• Description of methods you used.
• The results of the research.

❓ What are the 5 parts of an abstract?

Parts of an abstract depend on the contents and limitations of your research. The 5 main elements are:

• The introduction
• Research significance
• Method description

❓ What makes a good abstract in a research paper?

A good abstract is one that:

• Meets all the requirements.
• Establishes the problem and main issues of the research.
• Describes the methods you used during the analysis.
• Showcases results of the study.
• Provides a clear conclusion.

❓ How long should my abstract be?

An average abstract is about 150-250 words long. You may often get strict limits that can go above or beyond these numbers. Your supervisor should provide the exact requirements for abstract length. So, make sure to double-check them.

Updated: Apr 9th, 2024

• Writing an Abstract: George Mason University
• Writing an Abstract for Your Research Paper: University of Wisconsin - Madison
• Writing an Abstract: Australian National University
• The Abstract: The University of Toronto

Writing an Abstract for Your Research Paper

Definition and Purpose of Abstracts

An abstract is a short summary of your (published or unpublished) research paper, usually about a paragraph (c. 6-7 sentences, 150-250 words) long. A well-written abstract serves multiple purposes:

• an abstract lets readers get the gist or essence of your paper or article quickly, in order to decide whether to read the full paper;
• an abstract prepares readers to follow the detailed information, analyses, and arguments in your full paper;
• and, later, an abstract helps readers remember key points from your paper.

It’s also worth remembering that search engines and bibliographic databases use abstracts, as well as the title, to identify key terms for indexing your published paper. So what you include in your abstract and in your title are crucial for helping other researchers find your paper or article.

If you are writing an abstract for a course paper, your professor may give you specific guidelines for what to include and how to organize your abstract. Similarly, academic journals often have specific requirements for abstracts. So in addition to following the advice on this page, you should be sure to look for and follow any guidelines from the course or journal you’re writing for.

The Contents of an Abstract

Abstracts contain most of the following kinds of information in brief form. The body of your paper will, of course, develop and explain these ideas much more fully. As you will see in the samples below, the proportion of your abstract that you devote to each kind of information—and the sequence of that information—will vary, depending on the nature and genre of the paper that you are summarizing in your abstract. And in some cases, some of this information is implied, rather than stated explicitly. The Publication Manual of the American Psychological Association , which is widely used in the social sciences, gives specific guidelines for what to include in the abstract for different kinds of papers—for empirical studies, literature reviews or meta-analyses, theoretical papers, methodological papers, and case studies.

Here are the typical kinds of information found in most abstracts:

• the context or background information for your research; the general topic under study; the specific topic of your research
• the central questions or statement of the problem your research addresses
• what’s already known about this question, what previous research has done or shown
• the main reason(s) , the exigency, the rationale , the goals for your research—Why is it important to address these questions? Are you, for example, examining a new topic? Why is that topic worth examining? Are you filling a gap in previous research? Applying new methods to take a fresh look at existing ideas or data? Resolving a dispute within the literature in your field? . . .
• your research and/or analytical methods
• your main findings , results , or arguments
• the significance or implications of your findings or arguments.

Your abstract should be intelligible on its own, without a reader’s having to read your entire paper. And in an abstract, you usually do not cite references—most of your abstract will describe what you have studied in your research and what you have found and what you argue in your paper. In the body of your paper, you will cite the specific literature that informs your research.

When to Write Your Abstract

Although you might be tempted to write your abstract first because it will appear as the very first part of your paper, it’s a good idea to wait to write your abstract until after you’ve drafted your full paper, so that you know what you’re summarizing.

What follows are some sample abstracts in published papers or articles, all written by faculty at UW-Madison who come from a variety of disciplines. We have annotated these samples to help you see the work that these authors are doing within their abstracts.

Choosing Verb Tenses within Your Abstract

The social science sample (Sample 1) below uses the present tense to describe general facts and interpretations that have been and are currently true, including the prevailing explanation for the social phenomenon under study. That abstract also uses the present tense to describe the methods, the findings, the arguments, and the implications of the findings from their new research study. The authors use the past tense to describe previous research.

The humanities sample (Sample 2) below uses the past tense to describe completed events in the past (the texts created in the pulp fiction industry in the 1970s and 80s) and uses the present tense to describe what is happening in those texts, to explain the significance or meaning of those texts, and to describe the arguments presented in the article.

The science samples (Samples 3 and 4) below use the past tense to describe what previous research studies have done and the research the authors have conducted, the methods they have followed, and what they have found. In their rationale or justification for their research (what remains to be done), they use the present tense. They also use the present tense to introduce their study (in Sample 3, “Here we report . . .”) and to explain the significance of their study (In Sample 3, This reprogramming . . . “provides a scalable cell source for. . .”).

Sample Abstract 1

From the social sciences.

Reporting new findings about the reasons for increasing economic homogamy among spouses

Gonalons-Pons, Pilar, and Christine R. Schwartz. “Trends in Economic Homogamy: Changes in Assortative Mating or the Division of Labor in Marriage?” Demography , vol. 54, no. 3, 2017, pp. 985-1005.

Sample Abstract 2

From the humanities.

Analyzing underground pulp fiction publications in Tanzania, this article makes an argument about the cultural significance of those publications

Emily Callaci. “Street Textuality: Socialism, Masculinity, and Urban Belonging in Tanzania’s Pulp Fiction Publishing Industry, 1975-1985.” Comparative Studies in Society and History , vol. 59, no. 1, 2017, pp. 183-210.

Sample Abstract/Summary 3

From the sciences.

Reporting a new method for reprogramming adult mouse fibroblasts into induced cardiac progenitor cells

Lalit, Pratik A., Max R. Salick, Daryl O. Nelson, Jayne M. Squirrell, Christina M. Shafer, Neel G. Patel, Imaan Saeed, Eric G. Schmuck, Yogananda S. Markandeya, Rachel Wong, Martin R. Lea, Kevin W. Eliceiri, Timothy A. Hacker, Wendy C. Crone, Michael Kyba, Daniel J. Garry, Ron Stewart, James A. Thomson, Karen M. Downs, Gary E. Lyons, and Timothy J. Kamp. “Lineage Reprogramming of Fibroblasts into Proliferative Induced Cardiac Progenitor Cells by Defined Factors.” Cell Stem Cell , vol. 18, 2016, pp. 354-367.

Sample Abstract 4, a Structured Abstract

Reporting results about the effectiveness of antibiotic therapy in managing acute bacterial sinusitis, from a rigorously controlled study

Note: This journal requires authors to organize their abstract into four specific sections, with strict word limits. Because the headings for this structured abstract are self-explanatory, we have chosen not to add annotations to this sample abstract.

Wald, Ellen R., David Nash, and Jens Eickhoff. “Effectiveness of Amoxicillin/Clavulanate Potassium in the Treatment of Acute Bacterial Sinusitis in Children.” Pediatrics , vol. 124, no. 1, 2009, pp. 9-15.

“OBJECTIVE: The role of antibiotic therapy in managing acute bacterial sinusitis (ABS) in children is controversial. The purpose of this study was to determine the effectiveness of high-dose amoxicillin/potassium clavulanate in the treatment of children diagnosed with ABS.

METHODS : This was a randomized, double-blind, placebo-controlled study. Children 1 to 10 years of age with a clinical presentation compatible with ABS were eligible for participation. Patients were stratified according to age (<6 or ≥6 years) and clinical severity and randomly assigned to receive either amoxicillin (90 mg/kg) with potassium clavulanate (6.4 mg/kg) or placebo. A symptom survey was performed on days 0, 1, 2, 3, 5, 7, 10, 20, and 30. Patients were examined on day 14. Children’s conditions were rated as cured, improved, or failed according to scoring rules.

RESULTS: Two thousand one hundred thirty-five children with respiratory complaints were screened for enrollment; 139 (6.5%) had ABS. Fifty-eight patients were enrolled, and 56 were randomly assigned. The mean age was 6630 months. Fifty (89%) patients presented with persistent symptoms, and 6 (11%) presented with nonpersistent symptoms. In 24 (43%) children, the illness was classified as mild, whereas in the remaining 32 (57%) children it was severe. Of the 28 children who received the antibiotic, 14 (50%) were cured, 4 (14%) were improved, 4(14%) experienced treatment failure, and 6 (21%) withdrew. Of the 28children who received placebo, 4 (14%) were cured, 5 (18%) improved, and 19 (68%) experienced treatment failure. Children receiving the antibiotic were more likely to be cured (50% vs 14%) and less likely to have treatment failure (14% vs 68%) than children receiving the placebo.

CONCLUSIONS : ABS is a common complication of viral upper respiratory infections. Amoxicillin/potassium clavulanate results in significantly more cures and fewer failures than placebo, according to parental report of time to resolution.” (9)

Some Excellent Advice about Writing Abstracts for Basic Science Research Papers, by Professor Adriano Aguzzi from the Institute of Neuropathology at the University of Zurich:

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• Abstract Generator

Abstract generator lets you create an abstract for the research paper by using advanced AI technology.

This online abstract maker generates a title and precise overview of the given content with one click.

It generates an accurate article abstract by combining the most relevant and important phrases from the content of the article.

How to write an abstract for a research paper?

Here’s how you can generate the abstract of your content in the below easy steps:

• Type or copy-paste your text into the given input field.
• Alternatively, upload a file from the local storage of your system.
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• Click on the Generate button.
• Copy the results and paste them wherever you want in real-time.

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It takes the important key phrases from the content and combines them to create an accurate abstract with advanced AI.

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This feature lets you download the abstracted text in DOC format for future use just within a single click.

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This free text abstraction tool requires no signup or registration process to use it. Simply go the Editpad.org , search for the Abstract Generator, open it, and enter your text to create an abstract of any text within seconds.

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Abstract Generator

This Abstract Generator is basically a guideline for writing abstracts. We have also written an article on how to write abstracts. Go through the post and use our tools to create properly formatted abstracts. Note: An abstract should be between 100 - 250 words.

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• How to Write an Abstract

Expedite peer review, increase search-ability, and set the tone for your study

The abstract is your chance to let your readers know what they can expect from your article. Learn how to write a clear, and concise abstract that will keep your audience reading.

How your abstract impacts editorial evaluation and future readership

After the title , the abstract is the second-most-read part of your article. A good abstract can help to expedite peer review and, if your article is accepted for publication, it’s an important tool for readers to find and evaluate your work. Editors use your abstract when they first assess your article. Prospective reviewers see it when they decide whether to accept an invitation to review. Once published, the abstract gets indexed in PubMed and Google Scholar , as well as library systems and other popular databases. Like the title, your abstract influences keyword search results. Readers will use it to decide whether to read the rest of your article. Other researchers will use it to evaluate your work for inclusion in systematic reviews and meta-analysis. It should be a concise standalone piece that accurately represents your research. 

What to include in an abstract

The main challenge you’ll face when writing your abstract is keeping it concise AND fitting in all the information you need. Depending on your subject area the journal may require a structured abstract following specific headings. A structured abstract helps your readers understand your study more easily. If your journal doesn’t require a structured abstract it’s still a good idea to follow a similar format, just present the abstract as one paragraph without headings. 

Background or Introduction – What is currently known? Start with a brief, 2 or 3 sentence, introduction to the research area. 

Objectives or Aims – What is the study and why did you do it? Clearly state the research question you’re trying to answer.

Methods – What did you do? Explain what you did and how you did it. Include important information about your methods, but avoid the low-level specifics. Some disciplines have specific requirements for abstract methods. 

• CONSORT for randomized trials.
• STROBE for observational studies
• PRISMA for systematic reviews and meta-analyses

Results – What did you find? Briefly give the key findings of your study. Include key numeric data (including confidence intervals or p values), where possible.

Conclusions – What did you conclude? Tell the reader why your findings matter, and what this could mean for the ‘bigger picture’ of this area of research. 

Writing tips

The main challenge you may find when writing your abstract is keeping it concise AND convering all the information you need to.

• Keep it concise and to the point. Most journals have a maximum word count, so check guidelines before you write the abstract to save time editing it later.
• Write for your audience. Are they specialists in your specific field? Are they cross-disciplinary? Are they non-specialists? If you’re writing for a general audience, or your research could be of interest to the public keep your language as straightforward as possible. If you’re writing in English, do remember that not all of your readers will necessarily be native English speakers.
• Focus on key results, conclusions and take home messages.
• Write your paper first, then create the abstract as a summary.
• Check the journal requirements before you write your abstract, eg. required subheadings.
• Include keywords or phrases to help readers search for your work in indexing databases like PubMed or Google Scholar.
• Double and triple check your abstract for spelling and grammar errors. These kind of errors can give potential reviewers the impression that your research isn’t sound, and can make it easier to find reviewers who accept the invitation to review your manuscript. Your abstract should be a taste of what is to come in the rest of your article.

Don’t

• Sensationalize your research.
• Speculate about where this research might lead in the future.
• Use abbreviations or acronyms (unless absolutely necessary or unless they’re widely known, eg. DNA).
• Repeat yourself unnecessarily, eg. “Methods: We used X technique. Results: Using X technique, we found…”
• Contradict anything in the rest of your manuscript.
• Include content that isn’t also covered in the main manuscript.
• Include citations or references.

Tip: How to edit your work

Editing is challenging, especially if you are acting as both a writer and an editor. Read our guidelines for advice on how to refine your work, including useful tips for setting your intentions, re-review, and consultation with colleagues.

• How to Write a Great Title
• How to Write Your Methods
• How to Report Statistics
• How to Write Discussions and Conclusions
• How to Edit Your Work

The contents of the Peer Review Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

The contents of the Writing Center are also available as a live, interactive training session, complete with slides, talking points, and activities. …

There’s a lot to consider when deciding where to submit your work. Learn how to choose a journal that will help your study reach its audience, while reflecting your values as a researcher…

What this handout is about

This handout provides definitions and examples of the two main types of abstracts: descriptive and informative. It also provides guidelines for constructing an abstract and general tips for you to keep in mind when drafting. Finally, it includes a few examples of abstracts broken down into their component parts.

What is an abstract?

An abstract is a self-contained, short, and powerful statement that describes a larger work. Components vary according to discipline. An abstract of a social science or scientific work may contain the scope, purpose, results, and contents of the work. An abstract of a humanities work may contain the thesis, background, and conclusion of the larger work. An abstract is not a review, nor does it evaluate the work being abstracted. While it contains key words found in the larger work, the abstract is an original document rather than an excerpted passage.

Why write an abstract?

You may write an abstract for various reasons. The two most important are selection and indexing. Abstracts allow readers who may be interested in a longer work to quickly decide whether it is worth their time to read it. Also, many online databases use abstracts to index larger works. Therefore, abstracts should contain keywords and phrases that allow for easy searching.

Say you are beginning a research project on how Brazilian newspapers helped Brazil’s ultra-liberal president Luiz Ignácio da Silva wrest power from the traditional, conservative power base. A good first place to start your research is to search Dissertation Abstracts International for all dissertations that deal with the interaction between newspapers and politics. “Newspapers and politics” returned 569 hits. A more selective search of “newspapers and Brazil” returned 22 hits. That is still a fair number of dissertations. Titles can sometimes help winnow the field, but many titles are not very descriptive. For example, one dissertation is titled “Rhetoric and Riot in Rio de Janeiro.” It is unclear from the title what this dissertation has to do with newspapers in Brazil. One option would be to download or order the entire dissertation on the chance that it might speak specifically to the topic. A better option is to read the abstract. In this case, the abstract reveals the main focus of the dissertation:

This dissertation examines the role of newspaper editors in the political turmoil and strife that characterized late First Empire Rio de Janeiro (1827-1831). Newspaper editors and their journals helped change the political culture of late First Empire Rio de Janeiro by involving the people in the discussion of state. This change in political culture is apparent in Emperor Pedro I’s gradual loss of control over the mechanisms of power. As the newspapers became more numerous and powerful, the Emperor lost his legitimacy in the eyes of the people. To explore the role of the newspapers in the political events of the late First Empire, this dissertation analyzes all available newspapers published in Rio de Janeiro from 1827 to 1831. Newspapers and their editors were leading forces in the effort to remove power from the hands of the ruling elite and place it under the control of the people. In the process, newspapers helped change how politics operated in the constitutional monarchy of Brazil.

From this abstract you now know that although the dissertation has nothing to do with modern Brazilian politics, it does cover the role of newspapers in changing traditional mechanisms of power. After reading the abstract, you can make an informed judgment about whether the dissertation would be worthwhile to read.

Besides selection, the other main purpose of the abstract is for indexing. Most article databases in the online catalog of the library enable you to search abstracts. This allows for quick retrieval by users and limits the extraneous items recalled by a “full-text” search. However, for an abstract to be useful in an online retrieval system, it must incorporate the key terms that a potential researcher would use to search. For example, if you search Dissertation Abstracts International using the keywords “France” “revolution” and “politics,” the search engine would search through all the abstracts in the database that included those three words. Without an abstract, the search engine would be forced to search titles, which, as we have seen, may not be fruitful, or else search the full text. It’s likely that a lot more than 60 dissertations have been written with those three words somewhere in the body of the entire work. By incorporating keywords into the abstract, the author emphasizes the central topics of the work and gives prospective readers enough information to make an informed judgment about the applicability of the work.

When do people write abstracts?

• when submitting articles to journals, especially online journals
• when applying for research grants
• when writing a book proposal
• when completing the Ph.D. dissertation or M.A. thesis
• when writing a proposal for a conference paper
• when writing a proposal for a book chapter

Most often, the author of the entire work (or prospective work) writes the abstract. However, there are professional abstracting services that hire writers to draft abstracts of other people’s work. In a work with multiple authors, the first author usually writes the abstract. Undergraduates are sometimes asked to draft abstracts of books/articles for classmates who have not read the larger work.

Types of abstracts

There are two types of abstracts: descriptive and informative. They have different aims, so as a consequence they have different components and styles. There is also a third type called critical, but it is rarely used. If you want to find out more about writing a critique or a review of a work, see the UNC Writing Center handout on writing a literature review . If you are unsure which type of abstract you should write, ask your instructor (if the abstract is for a class) or read other abstracts in your field or in the journal where you are submitting your article.

Descriptive abstracts

A descriptive abstract indicates the type of information found in the work. It makes no judgments about the work, nor does it provide results or conclusions of the research. It does incorporate key words found in the text and may include the purpose, methods, and scope of the research. Essentially, the descriptive abstract describes the work being abstracted. Some people consider it an outline of the work, rather than a summary. Descriptive abstracts are usually very short—100 words or less.

Informative abstracts

The majority of abstracts are informative. While they still do not critique or evaluate a work, they do more than describe it. A good informative abstract acts as a surrogate for the work itself. That is, the writer presents and explains all the main arguments and the important results and evidence in the complete article/paper/book. An informative abstract includes the information that can be found in a descriptive abstract (purpose, methods, scope) but also includes the results and conclusions of the research and the recommendations of the author. The length varies according to discipline, but an informative abstract is rarely more than 10% of the length of the entire work. In the case of a longer work, it may be much less.

Here are examples of a descriptive and an informative abstract of this handout on abstracts . Descriptive abstract:

The two most common abstract types—descriptive and informative—are described and examples of each are provided.

Informative abstract:

Abstracts present the essential elements of a longer work in a short and powerful statement. The purpose of an abstract is to provide prospective readers the opportunity to judge the relevance of the longer work to their projects. Abstracts also include the key terms found in the longer work and the purpose and methods of the research. Authors abstract various longer works, including book proposals, dissertations, and online journal articles. There are two main types of abstracts: descriptive and informative. A descriptive abstract briefly describes the longer work, while an informative abstract presents all the main arguments and important results. This handout provides examples of various types of abstracts and instructions on how to construct one.

Which type should I use?

Your best bet in this case is to ask your instructor or refer to the instructions provided by the publisher. You can also make a guess based on the length allowed; i.e., 100-120 words = descriptive; 250+ words = informative.

How do I write an abstract?

The format of your abstract will depend on the work being abstracted. An abstract of a scientific research paper will contain elements not found in an abstract of a literature article, and vice versa. However, all abstracts share several mandatory components, and there are also some optional parts that you can decide to include or not. When preparing to draft your abstract, keep the following key process elements in mind:

• Reason for writing: What is the importance of the research? Why would a reader be interested in the larger work?
• Problem: What problem does this work attempt to solve? What is the scope of the project? What is the main argument/thesis/claim?
• Methodology: An abstract of a scientific work may include specific models or approaches used in the larger study. Other abstracts may describe the types of evidence used in the research.
• Results: Again, an abstract of a scientific work may include specific data that indicates the results of the project. Other abstracts may discuss the findings in a more general way.
• Implications: What changes should be implemented as a result of the findings of the work? How does this work add to the body of knowledge on the topic?

(This list of elements is adapted with permission from Philip Koopman, “How to Write an Abstract.” )

All abstracts include:

• A full citation of the source, preceding the abstract.
• The most important information first.
• The same type and style of language found in the original, including technical language.
• Key words and phrases that quickly identify the content and focus of the work.
• Clear, concise, and powerful language.

Abstracts may include:

• The thesis of the work, usually in the first sentence.
• Background information that places the work in the larger body of literature.
• The same chronological structure as the original work.

How not to write an abstract:

• Do not refer extensively to other works.
• Do not add information not contained in the original work.
• Do not define terms.

If you are abstracting your own writing

When abstracting your own work, it may be difficult to condense a piece of writing that you have agonized over for weeks (or months, or even years) into a 250-word statement. There are some tricks that you could use to make it easier, however.

Reverse outlining:

This technique is commonly used when you are having trouble organizing your own writing. The process involves writing down the main idea of each paragraph on a separate piece of paper– see our short video . For the purposes of writing an abstract, try grouping the main ideas of each section of the paper into a single sentence. Practice grouping ideas using webbing or color coding .

For a scientific paper, you may have sections titled Purpose, Methods, Results, and Discussion. Each one of these sections will be longer than one paragraph, but each is grouped around a central idea. Use reverse outlining to discover the central idea in each section and then distill these ideas into one statement.

Cut and paste:

To create a first draft of an abstract of your own work, you can read through the entire paper and cut and paste sentences that capture key passages. This technique is useful for social science research with findings that cannot be encapsulated by neat numbers or concrete results. A well-written humanities draft will have a clear and direct thesis statement and informative topic sentences for paragraphs or sections. Isolate these sentences in a separate document and work on revising them into a unified paragraph.

If you are abstracting someone else’s writing

When abstracting something you have not written, you cannot summarize key ideas just by cutting and pasting. Instead, you must determine what a prospective reader would want to know about the work. There are a few techniques that will help you in this process:

Identify key terms:

Search through the entire document for key terms that identify the purpose, scope, and methods of the work. Pay close attention to the Introduction (or Purpose) and the Conclusion (or Discussion). These sections should contain all the main ideas and key terms in the paper. When writing the abstract, be sure to incorporate the key terms.

Highlight key phrases and sentences:

Instead of cutting and pasting the actual words, try highlighting sentences or phrases that appear to be central to the work. Then, in a separate document, rewrite the sentences and phrases in your own words.

Don’t look back:

After reading the entire work, put it aside and write a paragraph about the work without referring to it. In the first draft, you may not remember all the key terms or the results, but you will remember what the main point of the work was. Remember not to include any information you did not get from the work being abstracted.

Revise, revise, revise

No matter what type of abstract you are writing, or whether you are abstracting your own work or someone else’s, the most important step in writing an abstract is to revise early and often. When revising, delete all extraneous words and incorporate meaningful and powerful words. The idea is to be as clear and complete as possible in the shortest possible amount of space. The Word Count feature of Microsoft Word can help you keep track of how long your abstract is and help you hit your target length.

Example 1: Humanities abstract

Kenneth Tait Andrews, “‘Freedom is a constant struggle’: The dynamics and consequences of the Mississippi Civil Rights Movement, 1960-1984” Ph.D. State University of New York at Stony Brook, 1997 DAI-A 59/02, p. 620, Aug 1998

This dissertation examines the impacts of social movements through a multi-layered study of the Mississippi Civil Rights Movement from its peak in the early 1960s through the early 1980s. By examining this historically important case, I clarify the process by which movements transform social structures and the constraints movements face when they try to do so. The time period studied includes the expansion of voting rights and gains in black political power, the desegregation of public schools and the emergence of white-flight academies, and the rise and fall of federal anti-poverty programs. I use two major research strategies: (1) a quantitative analysis of county-level data and (2) three case studies. Data have been collected from archives, interviews, newspapers, and published reports. This dissertation challenges the argument that movements are inconsequential. Some view federal agencies, courts, political parties, or economic elites as the agents driving institutional change, but typically these groups acted in response to the leverage brought to bear by the civil rights movement. The Mississippi movement attempted to forge independent structures for sustaining challenges to local inequities and injustices. By propelling change in an array of local institutions, movement infrastructures had an enduring legacy in Mississippi.

Now let’s break down this abstract into its component parts to see how the author has distilled his entire dissertation into a ~200 word abstract.

What the dissertation does This dissertation examines the impacts of social movements through a multi-layered study of the Mississippi Civil Rights Movement from its peak in the early 1960s through the early 1980s. By examining this historically important case, I clarify the process by which movements transform social structures and the constraints movements face when they try to do so.

How the dissertation does it The time period studied in this dissertation includes the expansion of voting rights and gains in black political power, the desegregation of public schools and the emergence of white-flight academies, and the rise and fall of federal anti-poverty programs. I use two major research strategies: (1) a quantitative analysis of county-level data and (2) three case studies.

What materials are used Data have been collected from archives, interviews, newspapers, and published reports.

Conclusion This dissertation challenges the argument that movements are inconsequential. Some view federal agencies, courts, political parties, or economic elites as the agents driving institutional change, but typically these groups acted in response to movement demands and the leverage brought to bear by the civil rights movement. The Mississippi movement attempted to forge independent structures for sustaining challenges to local inequities and injustices. By propelling change in an array of local institutions, movement infrastructures had an enduring legacy in Mississippi.

Keywords social movements Civil Rights Movement Mississippi voting rights desegregation

Example 2: Science Abstract

Luis Lehner, “Gravitational radiation from black hole spacetimes” Ph.D. University of Pittsburgh, 1998 DAI-B 59/06, p. 2797, Dec 1998

The problem of detecting gravitational radiation is receiving considerable attention with the construction of new detectors in the United States, Europe, and Japan. The theoretical modeling of the wave forms that would be produced in particular systems will expedite the search for and analysis of detected signals. The characteristic formulation of GR is implemented to obtain an algorithm capable of evolving black holes in 3D asymptotically flat spacetimes. Using compactification techniques, future null infinity is included in the evolved region, which enables the unambiguous calculation of the radiation produced by some compact source. A module to calculate the waveforms is constructed and included in the evolution algorithm. This code is shown to be second-order convergent and to handle highly non-linear spacetimes. In particular, we have shown that the code can handle spacetimes whose radiation is equivalent to a galaxy converting its whole mass into gravitational radiation in one second. We further use the characteristic formulation to treat the region close to the singularity in black hole spacetimes. The code carefully excises a region surrounding the singularity and accurately evolves generic black hole spacetimes with apparently unlimited stability.

This science abstract covers much of the same ground as the humanities one, but it asks slightly different questions.

Why do this study The problem of detecting gravitational radiation is receiving considerable attention with the construction of new detectors in the United States, Europe, and Japan. The theoretical modeling of the wave forms that would be produced in particular systems will expedite the search and analysis of the detected signals.

What the study does The characteristic formulation of GR is implemented to obtain an algorithm capable of evolving black holes in 3D asymptotically flat spacetimes. Using compactification techniques, future null infinity is included in the evolved region, which enables the unambiguous calculation of the radiation produced by some compact source. A module to calculate the waveforms is constructed and included in the evolution algorithm.

Results This code is shown to be second-order convergent and to handle highly non-linear spacetimes. In particular, we have shown that the code can handle spacetimes whose radiation is equivalent to a galaxy converting its whole mass into gravitational radiation in one second. We further use the characteristic formulation to treat the region close to the singularity in black hole spacetimes. The code carefully excises a region surrounding the singularity and accurately evolves generic black hole spacetimes with apparently unlimited stability.

Keywords gravitational radiation (GR) spacetimes black holes

Works consulted

We consulted these works while writing this handout. This is not a comprehensive list of resources on the handout’s topic, and we encourage you to do your own research to find additional publications. Please do not use this list as a model for the format of your own reference list, as it may not match the citation style you are using. For guidance on formatting citations, please see the UNC Libraries citation tutorial . We revise these tips periodically and welcome feedback.

Belcher, Wendy Laura. 2009. Writing Your Journal Article in Twelve Weeks: A Guide to Academic Publishing Success. Thousand Oaks, CA: Sage Press.

Koopman, Philip. 1997. “How to Write an Abstract.” Carnegie Mellon University. October 1997. http://users.ece.cmu.edu/~koopman/essays/abstract.html .

Lancaster, F.W. 2003. Indexing And Abstracting in Theory and Practice , 3rd ed. London: Facet Publishing.

You may reproduce it for non-commercial use if you use the entire handout and attribute the source: The Writing Center, University of North Carolina at Chapel Hill

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How To Write an Abstract for Any Subject and Publication (With Examples)

Table of contents

Christian Rigg

An abstract is a short summary of a longer work, such as a study or research paper. The goal is to provide readers with an overview of the purpose, methodology, results, conclusion, and importance of this text.

As a writing coach and part-time academic editor and translator, I’ve read hundreds of abstracts and helped authors draft and refine dozens more. I’ve found that, when writing an abstract, the greatest difficulty lies in balancing brevity, detail, and accessibility.

Fortunately, there’s a simple formula you can use to write a solid abstract for publication, regardless of the subject. What’s more, you can leverage AI to help you write a clear, concise abstract — without losing your voice or sounding unprofessional.

Below you’ll find step-by-step instructions, best practices, examples, and a helpful checklist. 

Key Takeaways

• An abstract offers a succinct overview of the aims, results, and importance of your research.
• Check submission guidelines, write clearly and concisely, and use language to “guide” readers through your abstract. 
• The IMRaD (Introduction, Methodology, Results, and Discussion) approach is simple and effective. 
• More and more authors are using AI to do the heavy lifting. With the right prompts, AI can save you time and create a cohesive abstract.

Writing an abstract: First steps and best practices

Keep the following in mind as you write your abstract:

• If you’re submitting to a publication , check for specific guidelines regarding overall length, format, keywords, and the presence or absence of section headings (e.g. “Purpose”). Follow these guidelines exactly.
• Write concisely and clearly . If you struggle to write concisely, consider using an AI-writing assistant like Wordtune . Simply select text to receive suggestions on how to write a sentence or paragraph more concisely without losing any value.
• Make your abstract self-contained . Don’t refer to passages in your article or research. If you must include terms that your audience may not be familiar with, such as highly technical jargon or concepts borrowed from another field, offer a brief definition.
• Use connecting phrases like “for this reason,” “as a result,” and “this led us” to “guide” the reader through your abstract and help them see the connections between your research goal, methodology, results, and conclusions. ‍
• Read abstracts on similar studies . This gives you a good benchmark and can help you get started. If you’re submitting your abstract to a particular publication, it also gives you a good idea of the type of language and structure they prefer.

Get Wordtune for free > Get Wordtune for free >

How to write an abstract: The IMRaD Structure

IMRaD stands for Introduction, Methodology, Results, and Discussion (or Conclusion). 

It’s the most common way to structure a research paper and a very simple way to approach your abstract. In some cases, authors even include these section headings in their abstracts. 

Step One: Introduction

Length : About 25% of your abstract

Purpose : Provide context for your research and describe your research objectives. 

Start by introducing your topic. There are two main parts to this:

• Your research question stated simply and straightforwardly (what missing knowledge does your study aim to answer?). You can use words like “investigate,” “review,” “test,” “analyze,” “study,” and “evaluate” to make it clear how your work relates to the context.
• A brief overview of the academic, historical, social, or scientific context. This helps the reader understand the importance and relevance of your work. In many cases, starting with context before your research question makes more sense, so feel free to write in that order. 

Regarding context, consider the following: 

For example:

Psychologists and neuroscientists have long studied the role of sleep in the formation of new memories. Previous research into how sleep affects memory has often struggled because it’s difficult to measure the quality, stages, and overall impact of sleep accurately. As a result, there’s ongoing debate in the scientific community , and recent research suggests sleep may not be as important as researchers once thought. In this study, we review the evidence and offer a novel conclusion : the same mechanisms thought to mediate sleep-related memory formation also operate during waking hours, particularly quiet wakefulness.  In this example, several contextual cues are offered: it’s a long-standing topic in the literature; previous research is limited due to a specific issue , and there is active scientific debate . The section closes with the research aims: to review the evidence and offer a new conclusion. 

Step Two: Methodology

Purpose : Clearly describe what you did and highlight novelty. 

In this section, provide a clear description of your research methodology. While it’s important to be concise, make sure you’re not being vague. Mention specific frameworks and tools. 

‍ To explore the impact of social media on political engagement, we conducted a study with 200 participants, divided into two groups. The first was exposed to curated political content on social media, while the control group received a neutral feed. Our mixed-method approach combined quantitative engagement metrics analysis and qualitative interviews to assess changes in political participation.

There’s no need to provide an in-depth justification of your approach, although if it’s a novel one, it’s worth highlighting this and explaining what makes it appropriate. For example, " We chose this approach because it offers a clearer image of the structure of proteins involved in the transfer of electrons during cellular respiration ."

Finally, you can omit methodological limitations; we’ll cover these later. 

Step Three: Results

Length : About 35% of your abstract

Purpose : Provide a clear, specific account of your results. 

This section is arguably the most important (and interesting) part of your abstract.

Explain the results of your analysis in a specific and detailed fashion. This isn’t the time to be vague or bury the lead. For example:

“Our survey indicates a marked shift in sedimentary rock composition. In three locations, we observed significant erosion, and mineralogical analysis revealed a high concentration of quartz. Further analysis suggests two major events in the past 200 years, correlating with disturbances in the region.”

"Our survey of the Redstone Canyon region identified a marked shift in sedimentary rock composition from predominantly sandstone to shale, particularly evident in the lower strata. Quantitative analysis showed a 40% increase in shale content compared to previous surveys. In three distinct locations, we observed significant erosion, with up to two meters of topsoil displacement, primarily due to water runoff. Mineralogical analysis revealed an unexpectedly high concentration of quartz (up to 22%) in these eroded areas. Additionally, our seismic retrogression analysis suggests two major seismic events in the past 200 years, correlating with the observed stratification disturbances."

Incidentally, you don’t need to include all of your findings here, only those that will help the reader to understand the next section: your discussion and conclusion (i.e., what the results mean). This will help you keep the results section concise and relevant. 

Step Four: Discussion/Conclusion

Length : About 15%

Purpose : Present what new knowledge you’ve found and why it matters.

Bearing in mind your research question, give a clear account of your conclusions. What new knowledge has been gained? 

The simplest way to do this is in the present tense: “We conclude that…”

You should also briefly explain why this matters. What are the implications of your findings? Be specific and avoid making claims that aren’t directly supported by your research. 

If there are any important limitations (such as population or control group size), you can mention them now. This helps readers assess the credibility and generalizability of your findings. 

You can use these samples for inspiration.

They are divided into introduction , methodology , results , and conclusion.

The rising urbanization rate poses challenges to mental health, an issue garnering increasing attention in recent years. This study aims to analyze the impact of urban green spaces on the mental health of city dwellers. The focus is on how access to parks and natural environments within urban settings contributes to psychological well-being . For this purpose, we employed a cross-sectional survey methodology, targeting residents in three major cities with varying levels of green space availability. We used a combination of GIS mapping to determine green space distribution and structured questionnaires to assess mental health indicators among 1,000 participants . Our results show a clear correlation between access to green spaces and improved mental health outcomes. Residents with frequent access to parks reported 30% lower stress levels and a 25% reduction in symptoms related to anxiety and depression, compared to those with limited access. Additionally, our analysis revealed that green spaces in dense urban areas had a more significant impact than those in less populated districts . We conclude that urban green spaces play a crucial role in enhancing mental health. This underscores the importance of urban planning policies that prioritize green space development as a public health strategy. These findings have significant implications for city planning and public health policy, advocating for the integration of green spaces in urban development to foster mental well-being .

The phenomenon of antibiotic resistance is a growing concern in medical science. This study investigates the effectiveness of novel synthetic peptides as potential antibiotics against multi-drug resistant bacteria. The research specifically examines the impact of these peptides on the cellular integrity and replication processes of resistant bacterial strains . Our methodology involved in vitro testing of three newly synthesized peptides against a panel of bacteria known for high resistance to conventional antibiotics. The bacterial strains included methicillin-resistant Staphylococcus aureus (MRSA) and vancomycin-resistant Enterococci (VRE). We used a combination of microbiological assays and electron microscopy to evaluate the antibacterial activity and the cellular changes induced by the peptides . The results were promising, showing that two of the three peptides effectively inhibited the growth of MRSA and VRE at low concentrations. Electron microscopy revealed significant disruption of bacterial cell walls and membranes, leading to cell lysis. These peptides also demonstrated low toxicity in preliminary mammalian cell culture tests, suggesting a high therapeutic index . Our study provides promising evidence for the use of synthetic peptides in combating antibiotic-resistant bacteria. These findings open new avenues for developing effective treatments against infections caused by drug-resistant pathogens and highlight the potential of peptide-based therapies in future pharmaceutical applications .

The integration of artificial intelligence (AI) in education is a rapidly evolving area of study. This research explores the effectiveness of AI-driven personalized learning systems in enhancing student performance in high school mathematics. The study focuses on understanding how AI customization impacts learning outcomes compared to traditional teaching methods . We conducted a randomized controlled trial involving 500 high school students from five schools, divided into two groups. The experimental group used an AI-based learning platform that adapted to each student's learning pace and style, while the control group continued with standard classroom instruction. The study measured improvements in mathematical understanding and problem-solving skills over a six-month period . The results indicated a significant improvement in the AI group, with a 40% increase in test scores and a 35% rise in problem-solving abilities compared to the control group. Additionally, students using the AI system reported higher levels of engagement and satisfaction with the learning process . In conclusion, the use of AI-driven personalized learning systems shows considerable promise in enhancing educational outcomes in mathematics. This study suggests that AI personalization can be a valuable tool in modern educational strategies, potentially revolutionizing how subjects are taught and learned in schools .

What is the main objective of an abstract?

The goal of an abstract is to provide readers with a concise overview of the purpose, methodology, results, conclusion, and importance of a longer work, such as a research paper or study. 

How long should an abstract be?

Depending on the publication, an abstract should be anywhere from 150 to 250 words. 

What should an abstract include?

An abstract should include an introduction (context + research question), the methodology, the results, and a conclusion (what you found and why it matters).

IMRaD is a simple formula you can follow to write a great abstract for any topic and publication type. Simply follow the instructions above to write each section: Introduction, Methodology, Results, and Discussion/Conclusion.

Be careful to balance detail with brevity, as abstracts are meant to be a short overview of your study. If you struggle with writing concisely and clearly, consider using a writing aid like Wordtune to handle some of the heavy lifting. 

Want to learn more key writing tips? Check out these articles:

• How to Write Concisely and Effectively (+Examples)
• Transition Word Examples and How to Use Them Effectively
• How to Write a Research Paper (+Free AI Research Paper Writer)

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How to Write an Abstract (With Examples)

Sarah Oakley

Table of Contents

What is an abstract in a paper, how long should an abstract be, 5 steps for writing an abstract, examples of an abstract, how prowritingaid can help you write an abstract.

If you are writing a scientific research paper or a book proposal, you need to know how to write an abstract, which summarizes the contents of the paper or book.

When researchers are looking for peer-reviewed papers to use in their studies, the first place they will check is the abstract to see if it applies to their work. Therefore, your abstract is one of the most important parts of your entire paper.

In this article, we’ll explain what an abstract is, what it should include, and how to write one.

An abstract is a concise summary of the details within a report. Some abstracts give more details than others, but the main things you’ll be talking about are why you conducted the research, what you did, and what the results show.

When a reader is deciding whether to read your paper completely, they will first look at the abstract. You need to be concise in your abstract and give the reader the most important information so they can determine if they want to read the whole paper.

Remember that an abstract is the last thing you’ll want to write for the research paper because it directly references parts of the report. If you haven’t written the report, you won’t know what to include in your abstract.

If you are writing a paper for a journal or an assignment, the publication or academic institution might have specific formatting rules for how long your abstract should be. However, if they don’t, most abstracts are between 150 and 300 words long.

A short word count means your writing has to be precise and without filler words or phrases. Once you’ve written a first draft, you can always use an editing tool, such as ProWritingAid, to identify areas where you can reduce words and increase readability.

If your abstract is over the word limit, and you’ve edited it but still can’t figure out how to reduce it further, your abstract might include some things that aren’t needed. Here’s a list of three elements you can remove from your abstract:

Discussion : You don’t need to go into detail about the findings of your research because your reader will find your discussion within the paper.

Definition of terms : Your readers are interested the field you are writing about, so they are likely to understand the terms you are using. If not, they can always look them up. Your readers do not expect you to give a definition of terms in your abstract.

References and citations : You can mention there have been studies that support or have inspired your research, but you do not need to give details as the reader will find them in your bibliography.

Good writing = better grades

ProWritingAid will help you improve the style, strength, and clarity of all your assignments.

If you’ve never written an abstract before, and you’re wondering how to write an abstract, we’ve got some steps for you to follow. It’s best to start with planning your abstract, so we’ve outlined the details you need to include in your plan before you write.

Remember to consider your audience when you’re planning and writing your abstract. They are likely to skim read your abstract, so you want to be sure your abstract delivers all the information they’re expecting to see at key points.

1. What Should an Abstract Include?

Abstracts have a lot of information to cover in a short number of words, so it’s important to know what to include. There are three elements that need to be present in your abstract:

Your context is the background for where your research sits within your field of study. You should briefly mention any previous scientific papers or experiments that have led to your hypothesis and how research develops in those studies.

Your hypothesis is your prediction of what your study will show. As you are writing your abstract after you have conducted your research, you should still include your hypothesis in your abstract because it shows the motivation for your paper.

Throughout your abstract, you also need to include keywords and phrases that will help researchers to find your article in the databases they’re searching. Make sure the keywords are specific to your field of study and the subject you’re reporting on, otherwise your article might not reach the relevant audience.

2. Can You Use First Person in an Abstract?

You might think that first person is too informal for a research paper, but it’s not. Historically, writers of academic reports avoided writing in first person to uphold the formality standards of the time. However, first person is more accepted in research papers in modern times.

If you’re still unsure whether to write in first person for your abstract, refer to any style guide rules imposed by the journal you’re writing for or your teachers if you are writing an assignment.

3. Abstract Structure

Some scientific journals have strict rules on how to structure an abstract, so it’s best to check those first. If you don’t have any style rules to follow, try using the IMRaD structure, which stands for Introduction, Methodology, Results, and Discussion.

Following the IMRaD structure, start with an introduction. The amount of background information you should include depends on your specific research area. Adding a broad overview gives you less room to include other details. Remember to include your hypothesis in this section.

The next part of your abstract should cover your methodology. Try to include the following details if they apply to your study:

What type of research was conducted?

How were the test subjects sampled?

What were the sample sizes?

What was done to each group?

How long was the experiment?

How was data recorded and interpreted?

Following the methodology, include a sentence or two about the results, which is where your reader will determine if your research supports or contradicts their own investigations.

The results are also where most people will want to find out what your outcomes were, even if they are just mildly interested in your research area. You should be specific about all the details but as concise as possible.

The last few sentences are your conclusion. It needs to explain how your findings affect the context and whether your hypothesis was correct. Include the primary take-home message, additional findings of importance, and perspective. Also explain whether there is scope for further research into the subject of your report.

Your conclusion should be honest and give the reader the ultimate message that your research shows. Readers trust the conclusion, so make sure you’re not fabricating the results of your research. Some readers won’t read your entire paper, but this section will tell them if it’s worth them referencing it in their own study.

4. How to Start an Abstract

The first line of your abstract should give your reader the context of your report by providing background information. You can use this sentence to imply the motivation for your research.

You don’t need to use a hook phrase or device in your first sentence to grab the reader’s attention. Your reader will look to establish relevance quickly, so readability and clarity are more important than trying to persuade the reader to read on.

5. How to Format an Abstract

Most abstracts use the same formatting rules, which help the reader identify the abstract so they know where to look for it.

Here’s a list of formatting guidelines for writing an abstract:

Stick to one paragraph

Use block formatting with no indentation at the beginning

Put your abstract straight after the title and acknowledgements pages

Use present or past tense, not future tense

There are two primary types of abstract you could write for your paper—descriptive and informative.

An informative abstract is the most common, and they follow the structure mentioned previously. They are longer than descriptive abstracts because they cover more details.

Descriptive abstracts differ from informative abstracts, as they don’t include as much discussion or detail. The word count for a descriptive abstract is between 50 and 150 words.

Here is an example of an informative abstract:

A growing trend exists for authors to employ a more informal writing style that uses “we” in academic writing to acknowledge one’s stance and engagement. However, few studies have compared the ways in which the first-person pronoun “we” is used in the abstracts and conclusions of empirical papers. To address this lacuna in the literature, this study conducted a systematic corpus analysis of the use of “we” in the abstracts and conclusions of 400 articles collected from eight leading electrical and electronic (EE) engineering journals. The abstracts and conclusions were extracted to form two subcorpora, and an integrated framework was applied to analyze and seek to explain how we-clusters and we-collocations were employed. Results revealed whether authors’ use of first-person pronouns partially depends on a journal policy. The trend of using “we” showed that a yearly increase occurred in the frequency of “we” in EE journal papers, as well as the existence of three “we-use” types in the article conclusions and abstracts: exclusive, inclusive, and ambiguous. Other possible “we-use” alternatives such as “I” and other personal pronouns were used very rarely—if at all—in either section. These findings also suggest that the present tense was used more in article abstracts, but the present perfect tense was the most preferred tense in article conclusions. Both research and pedagogical implications are proffered and critically discussed.

Wang, S., Tseng, W.-T., & Johanson, R. (2021). To We or Not to We: Corpus-Based Research on First-Person Pronoun Use in Abstracts and Conclusions. SAGE Open, 11(2).

Here is an example of a descriptive abstract:

From the 1850s to the present, considerable criminological attention has focused on the development of theoretically-significant systems for classifying crime. This article reviews and attempts to evaluate a number of these efforts, and we conclude that further work on this basic task is needed. The latter part of the article explicates a conceptual foundation for a crime pattern classification system, and offers a preliminary taxonomy of crime.

Farr, K. A., & Gibbons, D. C. (1990). Observations on the Development of Crime Categories. International Journal of Offender Therapy and Comparative Criminology, 34(3), 223–237.

If you want to ensure your abstract is grammatically correct and easy to read, you can use ProWritingAid to edit it. The software integrates with Microsoft Word, Google Docs, and most web browsers, so you can make the most of it wherever you’re writing your paper.

Before you edit with ProWritingAid, make sure the suggestions you are seeing are relevant for your document by changing the document type to “Abstract” within the Academic writing style section.

You can use the Readability report to check your abstract for places to improve the clarity of your writing. Some suggestions might show you where to remove words, which is great if you’re over your word count.

We hope the five steps and examples we’ve provided help you write a great abstract for your research paper.

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• Published: 06 May 2024

APOE4 homozygozity represents a distinct genetic form of Alzheimer’s disease

• Juan Fortea   ORCID: orcid.org/0000-0002-1340-638X 1 , 2 , 3   na1 ,
• Jordi Pegueroles   ORCID: orcid.org/0000-0002-3554-2446 1 , 2 ,
• Daniel Alcolea   ORCID: orcid.org/0000-0002-3819-3245 1 , 2 ,
• Olivia Belbin   ORCID: orcid.org/0000-0002-6109-6371 1 , 2 ,
• Oriol Dols-Icardo   ORCID: orcid.org/0000-0003-2656-8748 1 , 2 ,
• Lídia Vaqué-Alcázar 1 , 4 ,
• Laura Videla   ORCID: orcid.org/0000-0002-9748-8465 1 , 2 , 3 ,
• Juan Domingo Gispert 5 , 6 , 7 , 8 , 9 ,
• Marc Suárez-Calvet   ORCID: orcid.org/0000-0002-2993-569X 5 , 6 , 7 , 8 , 9 ,
• Sterling C. Johnson   ORCID: orcid.org/0000-0002-8501-545X 10 ,
• Reisa Sperling   ORCID: orcid.org/0000-0003-1535-6133 11 ,
• Alexandre Bejanin   ORCID: orcid.org/0000-0002-9958-0951 1 , 2 ,
• Alberto Lleó   ORCID: orcid.org/0000-0002-2568-5478 1 , 2 &
• Víctor Montal   ORCID: orcid.org/0000-0002-5714-9282 1 , 2 , 12   na1  

Nature Medicine ( 2024 ) Cite this article

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• Alzheimer's disease
• Predictive markers

This study aimed to evaluate the impact of APOE4 homozygosity on Alzheimer’s disease (AD) by examining its clinical, pathological and biomarker changes to see whether APOE4 homozygotes constitute a distinct, genetically determined form of AD. Data from the National Alzheimer’s Coordinating Center and five large cohorts with AD biomarkers were analyzed. The analysis included 3,297 individuals for the pathological study and 10,039 for the clinical study. Findings revealed that almost all APOE4 homozygotes exhibited AD pathology and had significantly higher levels of AD biomarkers from age 55 compared to APOE3 homozygotes. By age 65, nearly all had abnormal amyloid levels in cerebrospinal fluid, and 75% had positive amyloid scans, with the prevalence of these markers increasing with age, indicating near-full penetrance of AD biology in APOE4 homozygotes. The age of symptom onset was earlier in APOE4 homozygotes at 65.1, with a narrower 95% prediction interval than APOE3 homozygotes. The predictability of symptom onset and the sequence of biomarker changes in APOE4 homozygotes mirrored those in autosomal dominant AD and Down syndrome. However, in the dementia stage, there were no differences in amyloid or tau positron emission tomography across haplotypes, despite earlier clinical and biomarker changes. The study concludes that APOE4 homozygotes represent a genetic form of AD, suggesting the need for individualized prevention strategies, clinical trials and treatments.

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Exceptionally low likelihood of Alzheimer’s dementia in APOE2 homozygotes from a 5,000-person neuropathological study

Association of APOE e2 genotype with Alzheimer’s and non-Alzheimer’s neurodegenerative pathologies

Apolipoprotein E and Alzheimer disease: pathobiology and targeting strategies

Data availability.

Access to tabular data from ADNI ( https://adni.loni.usc.edu/ ), OASIS ( https://oasis-brains.org/ ), A4 ( https://ida.loni.usc.edu/collaboration/access/appLicense.jsp ) and NACC ( https://naccdata.org/ ) can be requested online, as publicly available databases. All requests will be reviewed by each studyʼs scientific board. Concrete inquiries to access the WRAP ( https://wrap.wisc.edu/data-requests-2/ ) and ALFA + ( https://www.barcelonabeta.org/en/alfa-study/about-the-alfa-study ) cohort data can be directed to each study team for concept approval and feasibility consultation. Requests will be reviewed to verify whether the request is subject to any intellectual property.

Code availability

All statistical analyses and raw figures were generated using R (v.4.2.2). We used the open-sourced R packages of ggplot2 (v.3.4.3), dplyr (v.1.1.3), ggstream (v.0.1.0), ggpubr (v.0.6), ggstatsplot (v.0.12), Rmisc (v.1.5.1), survival (v.3.5), survminer (v.0.4.9), gtsummary (v.1.7), epitools (v.0.5) and statsExpression (v.1.5.1). Rscripts to replicate our findings can be found at https://gitlab.com/vmontalb/apoe4-asdad (ref. 32 ). For neuroimaging analyses, we used Free Surfer (v.6.0) and ANTs (v.2.4.0).

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Acknowledgements

We acknowledge the contributions of several consortia that provided data for this study. We extend our appreciation to the NACC, the Alzheimer’s Disease Neuroimaging Initiative, The A4 Study, the ALFA Study, the Wisconsin Register for Alzheimer’s Prevention and the OASIS3 Project. Without their dedication to advancing Alzheimer’s disease research and their commitment to data sharing, this study would not have been possible. We also thank all the participants and investigators involved in these consortia for their tireless efforts and invaluable contributions to the field. We also thank the institutions that funded this study, the Fondo de Investigaciones Sanitario, Carlos III Health Institute, the Centro de Investigación Biomédica en Red sobre Enfermedades Neurodegenerativas and the Generalitat de Catalunya and La Caixa Foundation, as well as the NIH, Horizon 2020 and the Alzheimer’s Association, which was crucial for this research. Funding: National Institute on Aging. This study was supported by the Fondo de Investigaciones Sanitario, Carlos III Health Institute (INT21/00073, PI20/01473 and PI23/01786 to J.F., CP20/00038, PI22/00307 to A.B., PI22/00456 to M.S.-C., PI18/00435 to D.A., PI20/01330 to A.L.) and the Centro de Investigación Biomédica en Red sobre Enfermedades Neurodegenerativas Program 1, partly jointly funded by Fondo Europeo de Desarrollo Regional, Unión Europea, Una Manera de Hacer Europa. This work was also supported by the National Institutes of Health grants (R01 AG056850; R21 AG056974, R01 AG061566, R01 AG081394 and R61AG066543 to J.F., S10 OD025245, P30 AG062715, U54 HD090256, UL1 TR002373, P01 AG036694 and P50 AG005134 to R.S.; R01 AG027161, R01 AG021155, R01 AG037639, R01 AG054059; P50 AG033514 and P30 AG062715 to S.J.) and ADNI (U01 AG024904), the Department de Salut de la Generalitat de Catalunya, Pla Estratègic de Recerca I Innovació en Salut (SLT006/17/00119 to J.F.; SLT002/16/00408 to A.L.) and the A4 Study (R01 AG063689, U24 AG057437 to R.A.S). It was also supported by Fundación Tatiana Pérez de Guzmán el Bueno (IIBSP-DOW-2020-151 o J.F.) and Horizon 2020–Research and Innovation Framework Programme from the European Union (H2020-SC1-BHC-2018-2020 to J.F.; 948677 and 847648 to M.S.-C.). La Caixa Foundation (LCF/PR/GN17/50300004 to M.S.-C.) and EIT Digital (Grant 2021 to J.D.G.) also supported this work. The Alzheimer Association also participated in the funding of this work (AARG-22-923680 to A.B.) and A4/LEARN Study AA15-338729 to R.A.S.). O.D.-I. receives funding from the Alzheimer’s Association (AARF-22-924456) and the Jerome Lejeune Foundation postdoctoral fellowship.

Author information

These authors contributed equally: Juan Fortea, Víctor Montal.

Authors and Affiliations

Sant Pau Memory Unit, Hospital de la Santa Creu i Sant Pau - Biomedical Research Institute Sant Pau, Barcelona, Spain

Juan Fortea, Jordi Pegueroles, Daniel Alcolea, Olivia Belbin, Oriol Dols-Icardo, Lídia Vaqué-Alcázar, Laura Videla, Alexandre Bejanin, Alberto Lleó & Víctor Montal

Centro de Investigación Biomédica en Red de Enfermedades Neurodegenerativas. CIBERNED, Barcelona, Spain

Juan Fortea, Jordi Pegueroles, Daniel Alcolea, Olivia Belbin, Oriol Dols-Icardo, Laura Videla, Alexandre Bejanin, Alberto Lleó & Víctor Montal

Barcelona Down Medical Center, Fundació Catalana Síndrome de Down, Barcelona, Spain

Juan Fortea & Laura Videla

Department of Medicine, Faculty of Medicine and Health Sciences, Institute of Neurosciences, University of Barcelona, Barcelona, Spain

Lídia Vaqué-Alcázar

Barcelonaβeta Brain Research Center (BBRC), Pasqual Maragall Foundation, Barcelona, Spain

Juan Domingo Gispert & Marc Suárez-Calvet

Neurosciences Programme, IMIM - Hospital del Mar Medical Research Institute, Barcelona, Spain

Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona, Spain

Centro de Investigación Biomédica en Red Bioingeniería, Biomateriales y Nanomedicina. Instituto de Salud carlos III, Madrid, Spain

Centro Nacional de Investigaciones Cardiovasculares (CNIC), Madrid, Spain

Wisconsin Alzheimer’s Disease Research Center, University of Wisconsin-Madison School of Medicine and Public Health, Madison, WI, USA

Sterling C. Johnson

Brigham and Women’s Hospital Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA

Reisa Sperling

Barcelona Supercomputing Center, Barcelona, Spain

Víctor Montal

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Contributions

J.F. and V.M. conceptualized the research project and drafted the initial manuscript. V.M., J.P. and J.F. conducted data analysis, interpreted statistical findings and created visual representations of the data. O.B. and O.D.-I. provided valuable insights into the genetics of APOE. L.V., A.B. and L.V.-A. meticulously reviewed and edited the manuscript for clarity, accuracy and coherence. J.D.G., M.S.-C., S.J. and R.S. played pivotal roles in data acquisition and securing funding. A.L. and D.A. contributed to the study design, offering guidance and feedback on statistical analyses, and provided critical review of the paper. All authors carefully reviewed the manuscript, offering pertinent feedback that enhanced the study’s quality, and ultimately approved the final version.

Corresponding authors

Correspondence to Juan Fortea or Víctor Montal .

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Competing interests.

S.C.J. has served at scientific advisory boards for ALZPath, Enigma and Roche Diagnostics. M.S.-C. has given lectures in symposia sponsored by Almirall, Eli Lilly, Novo Nordisk, Roche Diagnostics and Roche Farma, received consultancy fees (paid to the institution) from Roche Diagnostics and served on advisory boards of Roche Diagnostics and Grifols. He was granted a project and is a site investigator of a clinical trial (funded to the institution) by Roche Diagnostics. In-kind support for research (to the institution) was received from ADx Neurosciences, Alamar Biosciences, Avid Radiopharmaceuticals, Eli Lilly, Fujirebio, Janssen Research & Development and Roche Diagnostics. J.D.G. has served as consultant for Roche Diagnostics, receives research funding from Hoffmann–La Roche, Roche Diagnostics and GE Healthcare, has given lectures in symposia sponsored by Biogen, Philips Nederlands, Esteve and Life Molecular Imaging and serves on an advisory board for Prothena Biosciences. R.S. has received personal consulting fees from Abbvie, AC Immune, Acumen, Alector, Bristol Myers Squibb, Janssen, Genentech, Ionis and Vaxxinity outside the submitted work. O.B. reported receiving personal fees from Adx NeuroSciences outside the submitted work. D.A. reported receiving personal fees for advisory board services and/or speaker honoraria from Fujirebio-Europe, Roche, Nutricia, Krka Farmacéutica and Esteve, outside the submitted work. A.L. has served as a consultant or on advisory boards for Almirall, Fujirebio-Europe, Grifols, Eisai, Lilly, Novartis, Roche, Biogen and Nutricia, outside the submitted work. J.F. reported receiving personal fees for service on the advisory boards, adjudication committees or speaker honoraria from AC Immune, Adamed, Alzheon, Biogen, Eisai, Esteve, Fujirebio, Ionis, Laboratorios Carnot, Life Molecular Imaging, Lilly, Lundbeck, Perha, Roche and outside the submitted work. O.B., D.A., A.L. and J.F. report holding a patent for markers of synaptopathy in neurodegenerative disease (licensed to Adx, EPI8382175.0). The remaining authors declare no competing interests.

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Fortea, J., Pegueroles, J., Alcolea, D. et al. APOE4 homozygozity represents a distinct genetic form of Alzheimer’s disease. Nat Med (2024). https://doi.org/10.1038/s41591-024-02931-w

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Marcus Riccelli now running unopposed for state Senate seat after last-minute opponent Ericka Lalka withdraws without explanation

State Rep. Marcus Riccelli, D-Spokane, will soon be a state senator, barring an insurgent write-in campaign, after his only opponent withdrew from the race Monday.

Ericka Lalka, who lost her race for Spokane School Board last year against incumbent Mike Wiser, had filed nine minutes before the deadline Friday to run as a Republican against Riccelli for the state Senate seat, which is being vacated by state Senate Majority Leader Andy Billig. By Monday, however, Lalka had withdrawn her candidacy.

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Parameters of the best fitting lunar ellipsoid based on GRAIL’s selenoid model

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• Published: 27 June 2023
• Volume 58 , pages 139–147, ( 2023 )

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• Kamilla Cziráki   ORCID: orcid.org/0009-0005-4162-4500 1 &
• Gábor Timár   ORCID: orcid.org/0000-0001-9675-6192 1  

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Since the Moon is less flattened than the Earth, most lunar GIS applications use a spherical datum. However, with the renaissance of lunar missions, it seems worthwhile to define an ellipsoid of revolution that better fits the selenoid. The main long-term benefit of this might be to make the lunar adaptation of methods already implemented in terrestrial GNSS and gravimetry easier and somewhat more accurate. In our work, we used the GRGM 1200A Lunar Geoid (Goossens et al. in A global degree and order 1200 model of the lunar gravity field using GRAIL mission data. In: Lunar and planetary science conference, Houston, TX, Abstract #1484, 2016; Lemoine et al. in Geophys Res Lett 41:3382–3389. http://dx.doi.org/10.1002/2014GL060027 , 2014), a 660th degree and order potential surface, developed in the frame of the GRAIL project. Samples were taken from the potential surface along a mesh that represents equal area pieces of the surface, using a Fibonacci sphere. We tried Fibonacci spheres with several numbers of points and also separately examined the effect of rotating the network for a given number of points on the estimated parameters. We estimated the best-fitting rotation ellipsoid’s semi-major axis and flatness data by minimizing the selenoid undulation values at the network points, which were obtained for a = 1,737,576.6 m and f = 0.000305. This parameter pair is already obtained for a 10,000 point grid, while the case of reducing the points of the mesh to 3000 does not cause a deviation in the axis data of more than 10 cm. As expected, the absolute value of the selenoid undulations have decreased compared to the values taken with respect to the spherical basal surface, but significant extreme values still remained as well.

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1 Introduction

The theoretical shape of a celestial body is defined by Gauss ( 1828 ) as the level surface of its gravitational field for a specific potential value. On the Earth, this potential surface is aligned with the mean sea level, but on other celestial bodies, such as the Moon, in the absence of sea, a potential value is chosen, compared to which about half of the Moon's surface is higher and half is lower. The resulting W = 2,821,713.3 m 2 * s −2 (Martinec & Pěč 1988 ) is the potential value for the selenoid surface. In addition to the theoretical definition of the shape of a celestial body, it is also essential to have a reference surface (a sphere or rotation ellipsoid in general) that can be described easily, with a few parameters, whose centre lies at the centre of mass of the body and which deviates as little as possible from the potential surface.

In our work, we have created a lunar rotation ellipsoid fitting this criteria using the GRGM 1200A Lunar Geoid from the GRAIL mission. To do this, we sampled the selenoid with a mesh of points representing the same areas and then used a program to find the semi-major axis-semi-minor axis pair that gave the best fit.

Such a rotating ellipsoid has significant practical benefits. It can be used well as a geodetic datum, and thus has a significant role as a base surface for various Geographic Informaton System (GIS) applications. What makes the problem of selenodetical datums relevant now is that lunar exploration is experiencing a renaissance, with not only the US but also the EU (in cooperation with the US) and China planning to send a series of space probes and landers to the Moon. NASA's Artemis program began this year, and its goal is to land on the Moon again, and perform research there. The Chinese Chang'e program has been going on for more than a decade, and its ultimate goal is to land a man on the far side of the Moon. During these missions, more time than ever before is planned to be spent on the lunar surface, during which positioning, and hence the lunar equivalent of Global Navigation Satellite System (GNSS), will play a major role. Since the basic data for GNSS applications is always the ellipsoid of revolution that best approximates the geometric shape on Earth, the simplest lunar application of these requires the parameters of the ellipsoidal approximation of the solenoid.

For LunaNet (NASA 2022 ), which NASA plans to create for GIS applications, the reference surface is currently planned to be the Lunar Reference Frame Standard, a sphere with a radius of 1737.4 km (NASA 2008 ). However, in the future, mainly in the process of the migration of gravimetric applications developed on Earth and the equations of the terrestrial GNSS, it is conceivable that a rotational ellipsoid will replace it.

For the estimation of the ellipsoidal parameters, we used the latest and highest resolution selenoid-model, the GRGM 1200A Lunar Geoid, based on GRAIL (Fig. 1 ). This includes the coefficients of the spherical harmonical functions up to 660th degree and order (Goossens et al. 2016 ; Lemoine et al. 2014 ) and also provides direct data from the far side of the Moon.

GRGM 1200A above the r  = 1737.4 km reference sphere displayed in QGIS Source : Goossens et al. ( 2016 ), Lemoine et al. ( 2014 ), QGIS

Besides the selenoid model, sampling points were needed to perform the estimation. The aim was to define points that represent equal areas on a spherical surface.

The points were determined using the Fibonacci sphere (Fig. 2 ). This is a set of points that maps the Fibonacci spiral onto a sphere. To create this, the z-axis was first divided into as many parts as the number of sample points defined. This gives the latitudes, and the longitudes were determined by rotations calculated with the Fibonacci number (Appendix A).

Display of the 3000-point Fibonacci sphere in QGIS

This was then used to sample the selenoid model. The resulting database contains the coordinates of the points and the altitude of the selenoid above a reference surface (a sphere of radius 1737.4 km). From this, the ellipsoidal approximation was made in a Python program. The idea is to find a semi-major axis-semi-minor axis pair for which the sum of the squares of the undulations of the selenoid at the sample points is minimal.

Equation  1 : Method to calculate the best-fitting ellipsoid for an N-point Fibonacci sphere.

Since the semi-major axis-major axis pair cannot be any value, both must be in the vicinity of the lunar reference sphere, all calculations were only performed between 1734 and 39 kms in the program. In addition, several iterative steps were used, first determining the minimum at a resolution of only 100 m, then at a higher resolution in the vicinity of the resulting minimum ± 100 m, and so on down to a resolution of 10 cm, saving a lot of time.

This program was not only used once on a single grid, but we also tested how the number of points on the Fibonacci sphere affected the results, using 100, 300, 1000, 3000, 5000, 10,000 and 100,000 point spheres, performing the steps of the calculation described above.

The semi-major axes, semi-minor axes and flatnesses of the ellipsoids thus obtained are shown in the table below. The seven results are based on samples of 100, 300, 1000, 3000, 5000, 10,000 and 100,000 points, with an accuracy of 10 cm (Table 1 ).

The parameters estimated from 100,000 sampled points have the highest accuracy (this result is the same as the parameters obtained for 10,000 points), so the half major axis of the rotation ellipsoid optimally fitting the Moon has a major axis of 1,737,576.6 m, a minor axis of 1,737,046.8 m and a flatness of 3.05 * 10 –4 (Cziráki & Timár 2023 ).

5 Discussion

5.1 comparison of the most accurate result with other reference surfaces.

As shown in Table 2 , the parameters of the rotation ellipsoid we have estimated differ by 176.6 and 353.2 m from the best fitting sphere. The flattening is 3/10,000, which is quite small, the same value on Earth is roughly 33/10,000 (World Geodetic System, WGS84), a significantly larger deviation from the sphere. This is due to the Earth's much faster axial rotation, which not only affects its gravitational field but also distorts its physical shape.

Our results were also compared to the triaxial ellipsoid created in 2010. This is based on the Chang'e 1 and Lunar Prospector (Konopliv et al. 2001 ) data CE-1-LAM-LEVEL (Wang et al. 2010 ). As can be seen from Table 2 , the differences are 125.9, − 12.8 and − 112.8 ms respectively. These may be due to the fact that the two models describe different geometric bodies. Another important difference is that the selenoid models used to calculate the parameters of the two ellipsoids are not the same. In the case of CE-1-LAM-LEVEL, the primary source of the selenoid model is the 180 degree and order model of the Lunar Prospector mission (Wang et al. 2010 ), which is lower in resolution than the GRGM 1200A model we used, and the Lunar Prospector model does not have direct data from the far side of the Moon, while GRAIL provided data from the far side with the same resolution as the near side. The differences between the two ellipsoids could therefore be due to these factors.

5.2 Variation of results as a function of Fibonacci spheres with different numbers of points

A central element of our research was that we carried out the estimation with meshes containing different numbers of points. These also provide information on the minimum number of points at which the result does not differ or differs only marginally from the most accurate estimate.

This was not expected for the samples with few points, as they represented too large areas (e.g., 379,323 km 2 for the 100-point sphere). Nevertheless, no deviation of more than 1 m was observed in our original sample. In order to determine the uncertainties, the 100-point sphere was rotated above the selenoid model every 30 degrees, the results of which are presented in Sect.  5.3 .

The resolution of the GRGM 1200A selenoid model is roughly 16.54 km, so the aim was to perform the calculation with a Fibonacci sphere of similar resolution. The 100,000-point Fibonacci sphere is the closest to achieving this, with 1 point representing 379 km 2 . Of course, the two resolutions are not exactly the same, as the selenoid model does not provide data in equal areas, but they are still similar in magnitude.

An important result, however, is that the result obtained with a 100,000 point sphere is already obtained with a sample with a tenth of a point, and from the 3000 point sample onwards, there is no difference of more than 10 cm.

5.3 Effect of rotating the Fibonacci sphere on the results

The results obtained are influenced to some extent by the position of the sampling points relative to the selenoid model. The significance of this decreases as the number of points increases and becomes negligible. In order to quantify this effect, the 100- and 5000-point Fibonacci spheres were rotated every 30 degrees above the selenoid and the approximation was also performed with these samples.

As expected, there are significant variations (Figs. 3 ,  4 ), especially among the 100-point samples, with a deviation of 5.56 m for the semi-major axis and 7.54 m for the semi-minor axis, and differences of more than 10 m. At 5000 points, the differences are almost negligible, with a standard deviation of 0.09 m for the semi-major axis and 0.14 m for the semi-minor axis, and all differences are within 0.5 m.

Length of the semi-major axis of the fitted ellipsoid for spheres with different positions

Length of the semi-minor axis of the fitted ellipsoid for spheres with different positions

5.4 Histogram of selenoid undulations on the resulting ellipsoid

The histogram of the selenoid undulations is of interest for the resulting ellipsoid, and for the selenoid model as well. This is shown with 5 m intervals in Fig.  5 .

Histogram of the selenoid undulations at the points of a Fibonacci sphere of 100,000 points, and the density function of the normal distribution ( m  = −0.0147 m, σ  = 110 m) fitted to it

Fortunately, the expected value of the fitted normal distribution is 0, but there are significant outliers. These are mainly indicative of inequalities in the potential surface of the selenoid. For example, mass concentrations, mascons (Muller & Sjorgen 1968 ), which cause a variation of several hundred mgal, have such an effect on the shape of the potential surfaces, and it is therefore not surprising that such excursions are observed.

It is also interesting to note that the extremes are much larger than, for example, on the Earth, where the geoidundulation values do not exceed ± 110 m. And for the Moon, these values reach as high as ± 450 m. This is mainly due to the absence of active planeto-dynamics, which does not allow the formation of mass accretions of this magnitude on Earth. Without these, anomalies can persist on the Moon, which can affect the shape of the potential surfaces to such a large extent.

5.5 Map representation of the selenoid undulations

As can be seen in Fig.  6 , the outliers are localised, mainly in the vicinity of certain craters. The positive anomalies mainly occur near the two craters on the Moon's near side, Mare Serenitatis and Mare Imbrium. The largest negative anomalies are found at the South Pole Aitken and at the Mare Orientale craters.

The undulations of the selenoid visualised in QGIS

On the map representation of the undulations, the outliers characterise the selenoid model, not the ellipsoid, since the localised large anomalies are not significantly reduced by just one extra parameter. More information about the effect of the ellipsoid can be obtained by comparing Fig.  6 with Fig.  1 , which is basically a map of the selenoidal undulations with respect to the reference sphere. This shows that the ellipsoid has reduced the undulations somewhat in general, but most strikingly, it has almost completely eliminated the anomalies at the poles. This was expected, as the rotation ellipsoid should show the greatest improvement in this area compared to the sphere.

5.6 Definition of the ideal ellipsoid on Earth

Using the methods described in Chapter 3, and with some minor modifications, the ideally fitting ellipsoid of the geoid was also calculated. This is, of course, a very widely used existing ellipsoid, WGS84 (DMA 1984 ). The primary aim of the calculation is therefore not to create a "new" ellipsoid, but rather to see how well our method can reproduce the parameters of WGS84, essentially to check the calculation method used for the Moon.

The input data used was the geoid model grid of EGM96 (Lemoine et al. 1996 ), downloaded from https://www.agisoft.com/downloads/geoids/ . This takes into account the coefficients of the spherical harmonic functions up to 360 degrees and order. The geoid was sampled using the 100,000-point Fibonacci sphere.

The ideal ellipsoid for the geoid was also calculated to an accuracy of 10 cm. This, as expected, differs only minimally from the parameters of WGS 84. Its semi-major axis is 6,378,137.0 m and its semi-minor axis is 6,356,752.3142 m. For the ellipsoid we obtained, the former is 6,378,136.4 m and the latter 6,356,751.7 m.

6 Conclusion

In our research, we performed an ellipsoidal approximation of the lunar gravitational field, we searched for the rotational ellipsoid that deviates least from the Moon's specific potential surface, which defines the selenoid. In doing so, we sampled the GRGM1200A selenoid model using a Fibonacci sphere with points representing equal areas, and then with this database, we estimated the parameters of the ellipsoid using a program based on a least-squares approximation of the selenoid undulations.

The resulting ellipsoid has its centre at the centre of mass of the Moon, a semi-major axis of 1,737,576.6 m, a semi-minor axis of 1,737,046.8 m and a flattening of 0.000305. The ellipsoidal parameters were determined with an accuracy of 10 cm, using multiple samples.

In our research, we also performed the calculation for the Earth geoid, with the aim of showing that this method can give a good estimate of the ideally fitting ellipsoid. Since the parameters of this ellipsoid on Earth are known, we compared our results to it, and they were very close, with a deviation of only 60 cm.

In the future, we would like to extend our research to the Earth, and investigate the differences in best fitting ellipsoids using varying geoid models.

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Supported by the ÚNKP-22-6 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development and Innovation Fund.

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Cziráki, K., Timár, G. Parameters of the best fitting lunar ellipsoid based on GRAIL’s selenoid model. Acta Geod Geophys 58 , 139–147 (2023). https://doi.org/10.1007/s40328-023-00415-w

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Received : 20 March 2023

Accepted : 29 May 2023

Published : 27 June 2023

Issue Date : June 2023

DOI : https://doi.org/10.1007/s40328-023-00415-w

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