Statistics

Confidence Interval Calculator

Compute confidence intervals for a mean, a proportion, the difference between two means (Welch), or the difference between two proportions. Get the interval bounds, margin of error, critical value, standard error, and clear calculation steps.

Mean CI Proportion CI Welch CI Margin of error

Confidence Interval Estimator

Select a mode, enter your sample statistics, and calculate your CI instantly.

Tip: If you estimated the standard deviation from your sample (most cases), keep t interval selected. Use z interval only when σ is known from a stable process.
Wilson intervals are usually more reliable—especially for small n or when the proportion is near 0% or 100%.
This mode uses Welch’s method (no equal-variance assumption) and returns a confidence interval for (x̄₁ − x̄₂).
This mode returns a confidence interval for the difference in proportions (p̂₁ − p̂₂) using a standard normal approximation.
Confidence Critical z (two-tailed) Typical use
90%1.645Exploratory analysis
95%1.960Default reporting
99%2.576High assurance