Confidence Interval Calculator
Calculate a confidence interval for a sample mean, using the sample size, standard deviation and chosen confidence level.
Confidence interval
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Margin of error —
Standard error —
Assumes a known or estimated population standard deviation and a roughly normal sampling distribution (valid for n ≥ 30 by the Central Limit Theorem).
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How it works
CI = mean ± z × (σ ÷ √n)Frequently Asked Questions
How do I calculate a confidence interval?
Multiply the z-score for your confidence level by the standard error (standard deviation ÷ √sample size), then add and subtract from the mean: a sample mean of 50 with σ=10, n=100 at 95% confidence gives 50 ± 1.96, or (48.04, 51.96).
What does 95% confidence actually mean?
If you repeated the sampling many times and built an interval each time, 95% of those intervals would contain the true population mean. It is not a 95% chance the true mean lies in this one specific interval.
How does sample size affect the interval?
Larger samples shrink the interval because standard error scales with 1/√n — quadrupling your sample size halves the margin of error, which is why polls need large samples for tight precision.