How this calculator works
For a mean, the calculator uses a normal critical value and the standard error s / sqrt(n). For a proportion, it uses the Wilson score interval, which is usually more stable than the simple p +/- z standard error formula for modest samples or proportions close to 0% or 100%.
Example
If a sample mean is 100, the sample standard deviation is 15 and the sample size is 36, the standard error is 15 / sqrt(36) = 2.5. A 95% interval using 1.96 is about 100 +/- 4.9, or 95.1 to 104.9.
Common mistakes
Do not describe a 95% confidence interval as a 95% probability that the one calculated interval contains the true value. The confidence level describes the long-run method across repeated samples.
Interpretation warning
A confidence interval describes what would happen over repeated samples using the same method. It is not a guarantee, and it does not fix sampling bias, nonresponse, measurement error or a poor study design.
References
- NIST/SEMATECH e-Handbook: Confidence Limits for the Mean - mean interval formula, accessed 2026-05-17.
- NIST/SEMATECH e-Handbook: What are confidence intervals? - confidence interval interpretation, accessed 2026-05-17.
FAQ
What does a 95% confidence interval mean?
In repeated sampling with the same method, about 95% of such intervals would contain the true parameter. It does not mean there is a 95% probability that this one fixed interval contains the parameter.
When should I use the mean mode?
Use the mean mode when you have a sample mean, standard deviation and sample size for a numeric measurement.
Why use Wilson for proportions?
Wilson intervals often behave better than the simple Wald interval, especially when proportions are near 0 or 1 or sample sizes are modest.
Last reviewed: 2026-05-17