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Random sampling and random assignment made easy.

Research Randomizer is a free resource for researchers and students in need of a quick way to generate random numbers or assign participants to experimental conditions. This site can be used for a variety of purposes, including psychology experiments, medical trials, and survey research.


In some cases, you may wish to generate more than one set of numbers at a time (e.g., when randomly assigning people to experimental conditions in a "blocked" research design). If you wish to generate multiple sets of random numbers, simply enter the number of sets you want, and Research Randomizer will display all sets in the results.

Specify how many numbers you want Research Randomizer to generate in each set. For example, a request for 5 numbers might yield the following set of random numbers: 2, 17, 23, 42, 50.

Specify the lowest and highest value of the numbers you want to generate. For example, a range of 1 up to 50 would only generate random numbers between 1 and 50 (e.g., 2, 17, 23, 42, 50). Enter the lowest number you want in the "From" field and the highest number you want in the "To" field.

Selecting "Yes" means that any particular number will appear only once in a given set (e.g., 2, 17, 23, 42, 50). Selecting "No" means that numbers may repeat within a given set (e.g., 2, 17, 17, 42, 50). Please note: Numbers will remain unique only within a single set, not across multiple sets. If you request multiple sets, any particular number in Set 1 may still show up again in Set 2.

Sorting your numbers can be helpful if you are performing random sampling, but it is not desirable if you are performing random assignment. To learn more about the difference between random sampling and random assignment, please see the Research Randomizer Quick Tutorial.

Place Markers let you know where in the sequence a particular random number falls (by marking it with a small number immediately to the left). Examples: With Place Markers Off, your results will look something like this: Set #1: 2, 17, 23, 42, 50 Set #2: 5, 3, 42, 18, 20 This is the default layout Research Randomizer uses. With Place Markers Within, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p1=5, p2=3, p3=42, p4=18, p5=20 This layout allows you to know instantly that the number 23 is the third number in Set #1, whereas the number 18 is the fourth number in Set #2. Notice that with this option, the Place Markers begin again at p1 in each set. With Place Markers Across, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p6=5, p7=3, p8=42, p9=18, p10=20 This layout allows you to know that 23 is the third number in the sequence, and 18 is the ninth number over both sets. As discussed in the Quick Tutorial, this option is especially helpful for doing random assignment by blocks.

Please note: By using this service, you agree to abide by the SPN User Policy and to hold Research Randomizer and its staff harmless in the event that you experience a problem with the program or its results. Although every effort has been made to develop a useful means of generating random numbers, Research Randomizer and its staff do not guarantee the quality or randomness of numbers generated. Any use to which these numbers are put remains the sole responsibility of the user who generated them.

Note: By using Research Randomizer, you agree to its Terms of Service .

Generate accurate APA citations for free

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APA Formatting and Citation (7th Ed.) | Generator, Template, Examples

Published on November 6, 2020 by Raimo Streefkerk . Revised on August 23, 2022.

The 7th edition of the APA Publication Manual provides guidelines for clear communication , citing sources , and formatting documents. This article focuses on paper formatting.

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Throughout your paper, you need to apply the following APA format guidelines:

APA format (7th edition)

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Table of contents

How to set up apa format (with template), apa alphabetization guidelines, apa format template [free download], page header, headings and subheadings, reference page, tables and figures, frequently asked questions about apa format.

References are ordered alphabetically by the first author’s last name. If the author is unknown, order the reference entry by the first meaningful word of the title (ignoring articles: “the”, “a”, or “an”).

Why set up APA format from scratch if you can download Scribbr’s template for free?

Student papers and professional papers have slightly different guidelines regarding the title page, abstract, and running head. Our template is available in Word and Google Docs format for both versions.

In an APA Style paper, every page has a page header. For student papers, the page header usually consists of just a page number in the page’s top-right corner. For professional papers intended for publication, it also includes a running head .

A running head is simply the paper’s title in all capital letters. It is left-aligned and can be up to 50 characters in length. Longer titles are abbreviated .

APA running head (7th edition)

APA headings have five possible levels. Heading level 1 is used for main sections such as “ Methods ” or “ Results ”. Heading levels 2 to 5 are used for subheadings. Each heading level is formatted differently.

Want to know how many heading levels you should use, when to use which heading level, and how to set up heading styles in Word or Google Docs? Then check out our in-depth article on APA headings .

APA headings (7th edition)

The title page is the first page of an APA Style paper. There are different guidelines for student and professional papers.

Both versions include the paper title and author’s name and affiliation. The student version includes the course number and name, instructor name, and due date of the assignment. The professional version includes an author note and running head .

For more information on writing a striking title, crediting multiple authors (with different affiliations), and writing the author note, check out our in-depth article on the APA title page .

APA title page - student version (7th edition)

The abstract is a 150–250 word summary of your paper. An abstract is usually required in professional papers, but it’s rare to include one in student papers (except for longer texts like theses and dissertations).

The abstract is placed on a separate page after the title page . At the top of the page, write the section label “Abstract” (bold and centered). The contents of the abstract appear directly under the label. Unlike regular paragraphs, the first line is not indented. Abstracts are usually written as a single paragraph without headings or blank lines.

Directly below the abstract, you may list three to five relevant keywords . On a new line, write the label “Keywords:” (italicized and indented), followed by the keywords in lowercase letters, separated by commas.

APA abstract (7th edition)

APA Style does not provide guidelines for formatting the table of contents . It’s also not a required paper element in either professional or student papers. If your instructor wants you to include a table of contents, it’s best to follow the general guidelines.

Place the table of contents on a separate page between the abstract and introduction. Write the section label “Contents” at the top (bold and centered), press “Enter” once, and list the important headings with corresponding page numbers.

The APA reference page is placed after the main body of your paper but before any appendices . Here you list all sources that you’ve cited in your paper (through APA in-text citations ). APA provides guidelines for formatting the references as well as the page itself.

Creating APA Style references

Play around with the Scribbr Citation Example Generator below to learn about the APA reference format of the most common source types or generate APA citations for free with Scribbr’s APA Citation Generator .

Formatting the reference page

Write the section label “References” at the top of a new page (bold and centered). Place the reference entries directly under the label in alphabetical order.

Finally, apply a hanging indent , meaning the first line of each reference is left-aligned, and all subsequent lines are indented 0.5 inches.

APA reference page (7th edition)

Tables and figures are presented in a similar format. They’re preceded by a number and title and followed by explanatory notes (if necessary).

Use bold styling for the word “Table” or “Figure” and the number, and place the title on a separate line directly below it (in italics and title case). Try to keep tables clean; don’t use any vertical lines, use as few horizontal lines as possible, and keep row and column labels concise.

Keep the design of figures as simple as possible. Include labels and a legend if needed, and only use color when necessary (not to make it look more appealing).

Check out our in-depth article about table and figure notes to learn when to use notes and how to format them.

APA table (7th edition)

The easiest way to set up APA format in Word is to download Scribbr’s free APA format template for student papers or professional papers.

Alternatively, you can watch Scribbr’s 5-minute step-by-step tutorial or check out our APA format guide with examples.

APA Style papers should be written in a font that is legible and widely accessible. For example:

The same font and font size is used throughout the document, including the running head , page numbers, headings , and the reference page . Text in footnotes and figure images may be smaller and use single line spacing.

You need an APA in-text citation and reference entry . Each source type has its own format; for example, a webpage citation is different from a book citation .

Use Scribbr’s free APA Citation Generator to generate flawless citations in seconds or take a look at our APA citation examples .

Yes, page numbers are included on all pages, including the title page , table of contents , and reference page . Page numbers should be right-aligned in the page header.

To insert page numbers in Microsoft Word or Google Docs, click ‘Insert’ and then ‘Page number’.

APA format is widely used by professionals, researchers, and students in the social and behavioral sciences, including fields like education, psychology, and business.

Be sure to check the guidelines of your university or the journal you want to be published in to double-check which style you should be using.

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Streefkerk, R. (2022, August 23). APA Formatting and Citation (7th Ed.) | Generator, Template, Examples. Scribbr. Retrieved March 1, 2023, from https://www.scribbr.com/apa-style/format/

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A random number is a number chosen from a pool of limited or unlimited numbers that has no discernible pattern for prediction. The pool of numbers is almost always independent from each other. However, the pool of numbers may follow a specific distribution. For example, the height of the students in a school tends to follow a normal distribution around the median height. If the height of a student is picked at random, the picked number has a higher chance to be closer to the median height than being classified as very tall or very short. The random number generators above assume that the numbers generated are independent of each other, and will be evenly spread across the whole range of possible values.

A random number generator, like the ones above, is a device that can generate one or many random numbers within a defined scope. Random number generators can be hardware based or pseudo-random number generators. Hardware based random-number generators can involve the use of a dice, a coin for flipping, or many other devices.

A pseudo-random number generator is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. Computer based random number generators are almost always pseudo-random number generators. Yet, the numbers generated by pseudo-random number generators are not truly random. Likewise, our generators above are also pseudo-random number generators. The random numbers generated are sufficient for most applications yet they should not be used for cryptographic purposes. True random numbers are based on physical phenomena such as atmospheric noise, thermal noise, and other quantum phenomena. Methods that generate true random numbers also involve compensating for potential biases caused by the measurement process.

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Pen and paper pseudo-random number generator

How can I generate pseudo-random numbers using only pen and paper?

I took a test where all questions were to be marked as right or wrong, and while correct answers would be worth two points, an incorrect answer would subtract one point.

With that system, if you guess all questions randomly, your expected score should be something around 25% (50% for the half that you got right, minus 25% for those you got wrong).

While that will be not enough for passing the test, it can make a difference when you use that technique on the questions you have no idea how to answer, or which you have no time for a proper analysis (as responses in blank do not add or subtract anything from the final score), since test scores are used for classification.

That got me thinking on how to generate proper random responses for such a task, when all you have is a pen and paper.

For my specific case, it was a binary matter, so much simpler. But I wondered what about multiple choices, where the response set has five or six alternatives.

One simpler option for binary was to just set ' right for odd questions, wrong for even questions ', which should produce the same result (yes?).

But I still think this is an interesting question, and my math skills are not enough for the problem. I'm pretty sure that I'll have to mod some number as the final step for getting the actual option. I also thought about using some check digit algorithm on a less random seed, perhaps reusing the last result somehow as input for the next iteration (but I may end up on a non-randomic sequence by doing that).

math.stackexchange already has some questions on this, like this and this .

Of these the responses, I liked the most were @Aaron Toponce's , @coffeemath's and @vrugtehagel's . However, they do not fit the criteria I put for the question (well, none of them is a formula, in the conventional sense, at least)

The question tile was changed from Yet another pen and paper random number generator question to Pen and paper pseudo-random number generator because, after thinking for a while, I came to the conclusion that you can't generate random numbers with mathematics alone and no clocks or anything external , as the question's restrictions listed.

Given a seed and a formula or algorithm, the end results will always be the same, as mathematics is deterministic by nature.

Some of the solutions I pointed above add the nondeterministic element by selecting a point in a drawing, which is fine, but not what I was looking for.

So, the definition of a pseudo-random number generator in the context of this question becomes:

A formula or algorithm, that, given an initial seed, generates a non-cyclic sequence of digits. The distribution of the digits in the sequence should be balanced.

I have uploaded to gist the Notebook I used to play with the proposed solutions:


All mistakes (code or conceptual) there are my own. The solution authors are mentioned on the respective response sections, but I diverged a bit from each of them on the actual code.

Note: I know this is not StackOverflow, but I think sharing this would be interesting for other like-minded people.

Community's user avatar

3 Answers 3

I would use a linear congruential generator . Given a seed $X_n$ it returns $X_{n+1}=aX_n+c \pmod m$ for parameters $a,c,m$ . I would then take some low order bits of $X_{n+1}$ as the random number. The calculation is not much even with pen and paper. You could use a relatively small $m$ because you don't need many bits. You would like $m$ to be prime, but if it has some large factors that is probably not so bad for this use. $a$ should be near $\sqrt m$ and coprime to it. You can seed it with $X_0$ being your birthday or some such.

Ross Millikan's user avatar

Square roots

One solution would be to use the digits of the square root of a number, such that the square root is not an integer (perfect square).

In that case, the square root should be an irrational number, which is acyclic by definition.

Analyzing this option for the numbers below 100 (with digits for the integer part of the square root plus 100 digits after the dot), I found that the balance between the generated digits is not always fair.

For the actual generated series, the average of the standard deviation was 3.034, with a maximum of 15.044 and a maximum difference between min occurrences and max occurrences of 15 (avg 9.433).

That is, counting the occurrence of each digit on a square root (limited to 100 after the dot) and calculating the standard deviation, then doing that for all non-perfect squares below 100 and taking the average of these results, the result is 3.034.

For the series mod 5 (that is, each element mod 5, for the situations where there are 5 options to choose from), the average standard deviation was 4.139 with a maximum of 7.778 and max diff of 21 (avg 10.178).

For the series mod 2 (true/false), average standard deviation of 5.971, max of 21.213, max diff of 30 (specifically for mod 2 of the digits in the square root of 41, 0 appears 65 times, 1 appears only 35 times), average of 8.444.

I'm not accepting this as the answer for my own question because:

Here is a solution that just uses the exam paper itself to do the pen and paper calculations. First I’m going to give a simplified version for true/false questions then explain how you can convert it into multiple choice.

The first 8 true or false questions are your seed so you have to pick them for yourself. Now counting backwards from the last question answered look at the 4th , 5th, 6th and 8th answers if there is an odd number of trues then write true otherwise write false. Repeat this sequence until you run out of questions.

This will create a linear feedback shift register with a cycle time of 255 steps. A longer sequence can be made with a seed of 16 and counting back 4, 13, 15,16.

You can convert this for multiple choice by treating the choice as a pair of true false questions. A = TT b=TF c=FT d=FF

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  1. Research Randomizer

    Research Randomizer is a free resource for researchers and students in need of a quick way to generate random numbers or assign participants to experimental conditions. This site can be used for a variety of purposes, including psychology experiments, medical trials, and survey research.

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  5. Pen and paper pseudo-random number generator

    Given a seed X n it returns X n + 1 = a X n + c ( mod m) for parameters a, c, m. I would then take some low order bits of X n + 1 as the random number. The calculation is not much even with pen and paper. You could use a relatively small m because you don't need many bits.