Critical Value Calculator
Choose your distribution, confidence level, and number of tails to find the critical value for a hypothesis test or confidence interval.
What this calculator does
A critical value marks the boundary of the rejection region in a hypothesis test, or the multiplier used to build a confidence interval. This calculator finds the critical value for either the standard normal (z) distribution or the Student’s t-distribution, based on your chosen confidence level and whether the test is one-tailed or two-tailed.
How the calculation works
The calculator converts your confidence level into a significance level (alpha), splitting it between two tails or keeping it in one tail as you specify. For the z-distribution it inverts the standard normal cumulative distribution function using a high-accuracy rational approximation. For the t-distribution, it starts from that same z-value and applies the Cornish-Fisher expansion, which adjusts for the extra spread introduced by a finite number of degrees of freedom.
As degrees of freedom increase, the t critical value converges toward the z critical value. This tool is for general statistical and educational use.