Confidence Interval Calculator

Calculate a confidence interval for a mean

This calculator estimates a two-sided confidence interval around a sample mean. Enter the number of observations, the sample mean, a standard deviation, and the confidence level.

The calculation is:

confidence interval = sample mean ± z × (standard deviation / √sample size)

For example, a sample mean of 50, standard deviation of 10, and sample size of 100 produces a standard error of 1. At 95% confidence, the z-based interval is 50 ± 1.96, or 48.04 to 51.96.

How to interpret the interval

A 95% confidence interval does not mean there is a 95% probability that one already-computed interval contains a fixed population mean. Under the model, if the same sampling process were repeated many times, about 95% of the intervals produced by that procedure would contain the true mean.

The width communicates precision under the assumptions. Larger samples and lower variability create narrower intervals; higher confidence levels create wider intervals.

When the z-based calculation is appropriate

This implementation uses a normal critical value. It is most appropriate when the population standard deviation is known or the sample is large enough for the normal approximation to be reasonable.

If you estimate the standard deviation from a small sample, a Student's t interval is normally more appropriate. Complex sampling, clustered observations, heavy skew, dependence, and weighting can also require another method.

Ecommerce examples

• Estimate a range around mean order value for a defined customer cohort.
• Compare average satisfaction ratings only when the scale and sampling method support treating the mean as useful.
• Report an experimental effect with its interval, not only whether a threshold was crossed.
• Use intervals alongside business impact, sample quality, and the actual response distribution.

For survey proportions, use the margin of error calculator. To plan a study before collection, use the sample size calculator.

Source: NIST/SEMATECH e-Handbook of Statistical Methods.

Reviewed 15 July 2026 by the UserLoop editorial team.