Confidence Interval Calculator

Calculate confidence intervals for population means and proportions.

Result

Fill in the fields above, then press Calculate.

A confidence interval calculator determines the range within which a population parameter is likely to fall at a given confidence level.

Enter the sample mean, standard deviation, sample size, and desired confidence level. The calculator will compute the confidence interval bounds and margin of error using the z-distribution.

Examples

Survey result

Mean 50, std dev 10, n=100, 95% CI: 50 ± 1.96 × (10/10) = (48.04, 51.96)

Small sample

Mean 75, std dev 5, n=25, 99% CI: 75 ± 2.576 × (5/5) = (72.42, 77.58)

Large sample

Mean 100, std dev 15, n=400, 90% CI: 100 ± 1.645 × 0.75 = (98.77, 101.23)

Frequently Asked Questions

What is a confidence interval?
A confidence interval gives a range of values that is likely to contain the true population parameter. A 95% CI means that if we repeated the sampling many times, 95% of intervals would contain the true value.
How does sample size affect the interval?
Larger sample sizes produce narrower confidence intervals because the standard error (σ/√n) decreases as n increases.
When should I use a t-distribution instead?
Use a t-distribution when the sample size is small (typically n < 30) and the population standard deviation is unknown. This calculator uses the z-distribution, suitable for larger samples.
Related Calculators
Z-Score Calculator
Sample Size Calculator
P-Value Calculator
Standard Deviation Calculator

Quick Tips

  • •Double-check your inputs — small errors lead to incorrect results.
  • •Use a t-distribution instead when your sample size is below 30 and the population standard deviation is unknown.
  • •Increasing the sample size narrows the confidence interval for the same confidence level.