Confidence Interval Calculator
Compute a confidence interval for a population mean from a sample mean, standard deviation, and size. For samples of 30 or more the calculator uses the normal (z) critical value; for smaller samples with an unknown population standard deviation it uses the t distribution (Cornish–Fisher approximation). Enter a confidence level (90 / 95 / 98 / 99 % or custom) to get the margin of error and the lower and upper bounds, plus the standard error and critical value used. Everything runs locally in your browser.
Standard error = sd ÷ √n. For n ≥ 30 the critical value is the normal quantile z = Φ⁻¹(1 − α/2), computed by Newton's method on the error-function CDF (matches standard tables to ~1e-6). For n < 30 the critical value is the t quantile with ν = n − 1 degrees of freedom, approximated by the Cornish–Fisher expansion (accurate to a few thousandths at common levels); a z-based interval would be too narrow for small samples. Margin of error = critical × SE. The interval is mean ± margin. This is a statistical estimate, not a guarantee. Runs locally.