Confidence Interval Calculator
Enter a sample mean, a standard deviation, n and a confidence level. The page builds a two-sided z-interval for the mean.
How it works
The interval is x̄ ± z × (s / √n). s / √n is the standard error. z is the two-sided standard-normal quantile (1.96 at 95%).
This is a large-sample / known-σ approximation — it does not use the t distribution or a degrees-of-freedom correction. n must be at least 2.
A 95% interval is not a 95% chance that this one interval contains the mean; it is the long-run coverage of the method.
Formula
x̄ ± z × (s / √n)
Worked examples
A 95% interval
x̄ = 50, s = 10, n = 25 → 46.08 to 53.92
Useful notes
- For small n and unknown σ, a t-interval is more appropriate. This page stays with z and says so.
- s can be a sample SD or a known population σ — you choose which number to type.
FAQ
- What is a confidence interval for a mean?
A range built from the sample so that, in repeated sampling, the stated percentage of such ranges contain the true mean.
- Why z and not t?
This tool uses the normal approximation. A t-interval would be wider for small n. The formula is spelled out so you can see the assumption.
- What is the margin of error?
The term z × (s / √n) — half the width of the interval.
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