Statistics Calculators

Confidence Interval Calculator

Calculate the confidence interval for a population mean based on a sample mean, standard deviation and sample size.

Margin of error —

Lower bound —

Upper bound —

About the Confidence Interval Calculator

A confidence interval gives a range of plausible values for a population mean, based on a sample. A 95% confidence interval means that if you repeated the sampling many times, about 95% of the resulting intervals would contain the true population mean.

Formula: CI = x̄ ± z × (σ ÷ √n), using z = 1.645 (90%), 1.96 (95%) or 2.576 (99%)

Wider intervals result from smaller sample sizes or higher confidence levels; larger samples produce narrower, more precise intervals.