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Confidence Interval Calculator

Calculate a confidence interval for a mean, with the margin of error and z critical value.

95.1001 – 104.8999

95% confidence interval

  • ± 4.8999Margin of error
  • 2.5Standard error
  • 1.96z critical

How to use it

  1. Enter the sample statistics Mean, standard deviation and sample size.
  2. Pick a confidence level Commonly 90%, 95% or 99%.
  3. Read the interval The range, margin of error and z value.

Examples

100, 15, n=36 95.1–104.9
95% z 1.96

About this tool

A confidence interval puts error bars around an estimate, turning a single sample mean into a plausible range for the true value. This calculator builds one from your sample mean, standard deviation and size at the confidence level you choose.

It uses the normal approximation and also shows the margin of error and the z critical value behind it. Wider intervals mean more confidence but less precision — the trade-off at the heart of statistics. Everything runs in your browser.

Frequently asked questions

How is the interval calculated?

It uses the normal approximation — the mean plus or minus the z critical value times the standard error (sd ÷ √n).

What does a 95% interval mean?

If you repeated the sampling many times, about 95% of the intervals built this way would contain the true population mean.

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Updated June 15, 2026