Confidence Interval Calculator
Calculate a confidence interval for a sample mean.
Assumptions used in this calculation
- Z-distribution: Uses the Z (normal) distribution critical values rather than the t-distribution, which is a reasonable approximation for larger sample sizes but less precise for small samples.
About this calculator
A sample mean is only an estimate of the true population mean, and reporting it alone hides how much uncertainty surrounds that estimate; a confidence interval expresses that uncertainty as a range, but building one correctly requires the right critical value and dividing by the square root of the sample size, not the sample size itself. This calculator takes a sample mean, standard deviation, sample size and confidence level, then computes the interval as CI = sample mean ± Z × (standard deviation ÷ √n), using the Z (normal) distribution's critical value for the chosen confidence level. It uses the Z-distribution rather than the t-distribution, which is a reasonable approximation for larger sample sizes but understates uncertainty for small samples, where the t-distribution's fatter tails would give a wider, more accurate interval. Because the margin shrinks with the square root of n, quadrupling your sample size only halves the interval's width. That produces a statistically grounded range for the true mean instead of just reporting a single point estimate.
Worked example
Mean 50, sd 10, n=100, 95% confidence
Result: CI = 48.04 to 51.96
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