FreeToolStation

Margin of Error Calculator

How accurate a survey result is, given its sample size.

Statistics Calculators Free, no sign-up Runs in your browser

50% gives the widest margin, which is why pollsters quote it.

Optional. Narrows the margin when the sample is a large share of the whole group.

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Margin of error
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Result range
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Critical value
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Standard error
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With population correction
Sample sizeMargin of errorRange around the result
Margin of error covers sampling error only. It says nothing about a badly worded question, a biased sample or people who did not respond, and those are usually the larger problems with a survey.

About the Margin of Error Calculator

Margin of Error Calculator works out how precise a survey result is, given how many people were asked. It is the critical value times the standard error of the proportion, and it is why a poll reporting 52 per cent with a three point margin cannot distinguish that from 49 per cent.

The result percentage affects the margin, and fifty per cent is the worst case. That is why pollsters quote the margin at fifty: it is the largest it can be for that sample size, so no individual question in the survey has a wider one. A result of ninety per cent has a substantially narrower margin on the same sample.

The sample-size table shows the brutal arithmetic of precision. Halving the margin of error takes four times the sample, because the margin falls with the square root of n. Going from a thousand respondents to two thousand improves the margin by about thirty per cent, which is why national polls cluster around a thousand: beyond that, the cost rises much faster than the accuracy.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

Looking for something this does not cover? FreeToolsHub.org is another hub of free online tools that need no account, and it is worth a look if margin of error calculator is only part of what you are working on.

How to use the Margin of Error Calculator

  1. Choose confidence levelThe fields below change to match what you pick, so only the figures that matter to your case are asked for.
  2. Enter sample size, result (%) and population sizeDecimals are fine, and thousands separators are accepted and ignored.
  3. Read the margin of error, result range and critical valueThe figures update as you type. The Calculate button is there if you would rather press something, but nothing waits for it.
  4. Copy or check the resultCopy the summary with the copy button, or open the table to check it row by row.

Features

  • Shows margin of error, result range, critical value, standard error and with population correction together, so you are not running it twice
  • A results table you can read across
  • Updates as you type, with no button to press and no page reload
  • Copy the result in one click
  • Free, no sign-up, and it runs entirely in your browser

Who uses this tool

The margin of error calculator is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

  • Reporting a survey result honestly
  • Judging whether two poll results really differ
  • Deciding how many responses a survey needs
  • Applying the finite population correction to a small group

Frequently asked questions

Why is the margin quoted at 50%?

Because that is where it is widest. Quoting the worst case means no question in the survey has a larger margin than the headline figure.

Does margin of error cover bias?

No. It covers random sampling error only. A leading question or a sample that misses part of the population introduces error this cannot measure.

What is the population correction for?

Sampling 500 people out of 2,000 tells you more than 500 out of millions. The correction narrows the margin when the sample is a large share of the population.

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Checked and rebuilt on 2026-10-14. The method this calculator uses is described in the section above, and corrections go through the contact page.