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Confidence Interval Calculator

Calculate a confidence interval for a mean (from raw data or summary statistics) or for a proportion, at 90%, 95% or 99% confidence.

How to use

  1. 1Choose mean or proportion.
  2. 2Enter the data (or mean, SD and sample size), or successes and trials for a proportion.

How it's calculated

Mean: x̄ ± t* × s ÷ √n (t distribution with n − 1 df). Proportion: p̂ ± z* × √(p̂(1 − p̂) ÷ n) (Wald), plus the Wilson interval for small samples.

Frequently asked questions

What does a 95% confidence interval mean?

If you repeated the study many times, about 95% of intervals built this way would contain the true value.

Why use t instead of z for means?

Because the population standard deviation is estimated from the sample. For large samples t and z are almost identical.

Why show the Wilson interval?

The simple (Wald) interval is inaccurate for small samples or proportions near 0% or 100%; Wilson performs much better.