Confidence Interval Calculator

CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.

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How to use this calculator

  • Enter sample mean and standard deviation.
  • Enter sample size.
  • Pick confidence level.
  • Read CI bounds.

About this calculator

A 95% confidence interval means: if we repeated this sampling procedure many times, ~95% of CIs would contain the true population mean. Wider CI = less precision. Doubling sample size shrinks margin by √2 (~30%). Quadrupling halves margin. Common z-values: 80% → 1.282, 90% → 1.645, 95% → 1.96, 99% → 2.576. For small samples (n < 30), use the t-distribution instead — wider intervals at given confidence.

Frequently asked

CI vs. p-value?+
Two views of the same statistical evidence. CI quantifies precision; p tests whether 0 (or some null value) lies in the CI.
When to use t instead of z?+
When n < 30 and σ is estimated from sample. For n ≥ 30, t and z converge so z works. This calc uses z.
Wider CI is bad?+
Wider = less precise. To narrow: increase n or reduce σ. Confidence level (95% vs 99%) also affects width.
Does CI include the true mean?+
For each individual CI: maybe (95% chance under repeated sampling). Don't say "95% probability mean is in this CI" — that's a Bayesian credible interval, not a frequentist CI.
Sample size for 1-point margin?+
n ≈ (z × σ / margin)². For σ = 15, 95% CI, margin = 1: n ≈ (1.96 × 15)² ≈ 864.

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