Confidence Interval Calculator
Build a confidence interval for a mean from the sample mean, SD and size.
Results update as you type.
About this calculator
A confidence interval gives a range that is likely to contain the true population mean. This calculator uses the z-interval: mean ± z*·(σ / √n), where z* is the standard-normal critical value for your chosen confidence level. The z-interval is appropriate for large samples (roughly n ≥ 30) or when the population standard deviation is known; for small samples use a t-interval instead.
Frequently asked questions
What does a 95% confidence interval mean?
It means that if you repeated the sampling many times and built an interval each time, about 95% of those intervals would contain the true population mean. It does not mean there is a 95% probability the mean is in this one particular interval.
When should I use a t-interval instead?
Use a t-interval when the sample is small (roughly under 30) and the population standard deviation is unknown. The t-distribution has heavier tails, giving a slightly wider, more cautious interval than this z-based one.
Results are estimates for general guidance only, not financial, medical or tax advice.