FreeToolStation

Confidence Interval Calculator

A confidence interval for a mean or a proportion, t values included.

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

For a mean.

For a mean.

For a proportion.

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Confidence interval
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Lower bound
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Upper bound
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Margin of error
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Critical value
Confidence levelCritical valueMargin of errorInterval
A 95% interval does not mean a 95% chance the true value is inside this one. It means that if you repeated the sampling many times, about 95% of the intervals produced would contain it. The distinction matters when the result is reported to somebody.

About the Confidence Interval Calculator

Confidence Interval Calculator builds an interval around a sample mean or a sample proportion. The interval is the estimate plus and minus a margin of error, and the margin is a critical value times the standard error of the estimate.

For a mean from a small sample the critical value comes from the t distribution rather than the normal one, and the calculator uses the t table for up to thirty degrees of freedom. This matters: with eight observations the 95 per cent t value is 2.365 against the normal 1.96, so using z would produce an interval about twenty per cent too narrow. A too-narrow interval is a statement of more confidence than the data supports.

The interpretation is the part most often got wrong, and it is worth being precise about. A 95 per cent interval does not mean there is a 95 per cent chance the true value lies in this particular interval. It means the procedure produces intervals that contain the true value 95 per cent of the time. The true value is fixed; it is the interval that varies from sample to sample.

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? FreeToolStation.com is a second collection of the same kind of everyday tools, and it is worth a look if confidence interval calculator is only part of what you are working on.

How to use the Confidence Interval Calculator

  1. Choose for a and 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, sample mean and sample standard deviationDecimals are fine, and thousands separators are accepted and ignored.
  3. Read the confidence interval, lower bound and upper boundThe 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 confidence interval, lower bound, upper bound, margin of error and critical value 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 confidence interval 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 with a margin of error
  • Putting bounds on an experimental mean
  • Checking how much a larger sample would narrow the interval
  • Comparing 90, 95 and 99 per cent intervals on the same data

Frequently asked questions

When should I use t instead of z?

For a mean from a sample of fewer than about thirty, where the population standard deviation is unknown. That is the usual case, and the calculator does it automatically.

What does 95% confidence mean?

That the method produces intervals containing the true value 95 per cent of the time. It is a property of the procedure, not a probability about this one interval.

Why is my interval so wide?

Small samples and large variation both widen it. The margin shrinks with the square root of the sample size, so halving it takes four times the data.

If the confidence interval calculator is not quite what you need, these other free tools solve closely related problems, and there are 13 more in statistics calculators.

Z-Score Calculator

Z-score with percentile and tail probabilities.

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Variance Calculator

Sample and population variance with the full working.

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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.