Critical Value Calculator

About this calculator

A critical value is the cutoff point on a probability distribution — the z, Student's t, or chi-square distribution — beyond which a test statistic is considered extreme enough to reject the null hypothesis. It depends on the chosen significance level (α), such as 0.05, and on whether the test is one-tailed or two-tailed: a two-tailed test at α = 0.05 splits the 5% between both ends of the distribution, giving a different cutoff than a one-tailed test at the same α.

Researchers, statisticians, and students look up critical values to decide whether a computed test statistic is statistically significant, and to construct confidence intervals — the t-distribution is used instead of z when the sample size is small and the population standard deviation is unknown, while chi-square critical values are used for variance tests and goodness-of-fit tests.