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Confidence Interval Calculator

Enter the sample mean, the standard deviation and the sample size.

The population standard deviation, or the sample standard deviation if the sample is large (about 30 or more).

Confidence level

This result is an estimate only. Double-check important figures before relying on them.

How it is calculated

  • Standard error = standard deviation ÷ √n
  • Margin of error = z × standard error (z = 1.645, 1.96 or 2.576)
  • Interval = mean ± margin of error

To find how large a sample you need, use the sample size calculator.

Worked example

Mean 100, standard deviation 15, 36 observations, 95% level:

  • Standard error = 2.5, margin = 4.9
  • Interval = 95.1 to 104.9

Why your number may differ

With small samples a t-based interval is wider. The interval also assumes a random sample.

Frequently asked questions

What is a confidence interval?

A range that is likely to contain the true population mean. A 95% interval means that if you repeated the study many times, about 95% of the intervals would contain it.

What is the formula?

Mean ± z × standard deviation ÷ √n, where z is 1.645, 1.96 or 2.576 for 90%, 95% and 99%.

What about small samples?

For samples under about 30 with an unknown population standard deviation, a t-distribution gives a slightly wider interval. This calculator uses the normal (z) values.

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