What does a 95% confidence interval mean?

If you repeated the sampling many times, about 95% of the intervals built this way would contain the true population mean. It is not the probability that this one interval contains the mean.

This tool uses the z critical value, which is appropriate when the population standard deviation is known or the sample is large. For small samples with an estimated standard deviation a t-interval is slightly wider.

Confidence Interval Calculator

Q: How is the confidence interval calculated?

It uses the z-based formula mean ± z × (σ / √n), where z is the critical value for your chosen confidence level. For 95% confidence z is 1.96.

Mean ± margin of error at 80–99% confidence.

Confidence interval calculator

A confidence interval gives a range likely to contain the true population mean. This calculator uses mean ± z × (σ / √n), where z is the critical value for your chosen confidence level (1.96 for 95%).

Enter your sample statistics and confidence level — all maths happens locally in your browser.