Critical Value Calculator

Use this Critical Value Calculator to find the critical values for common statistical tests. This calculator supports Z, t, chi-square (χ²), and F-distributions. To use it, select your test statistic distribution from the dropdown menu. Then, enter the degrees of freedom if required and choose your significance level. Click Calculate to find the critical value(s) for your test.

For Z and t-tests, you can choose a two-tailed, left-tailed, or right-tailed test. This critical value calculator always returns a right-tailed critical value for chi-square and F distributions because those tests are inherently one-sided. (See the explanation below.) After the calculator, you’ll find more details about how to interpret the results and how this calculator works. See all my Statistical Calculators!

A critical value defines the boundary beyond which results are considered statistically significant. If your test statistic exceeds this value, you reject the null hypothesis. This calculator helps you identify the exact value for your significance level, test type, and distribution. Learn more in my article, Critical Values: Definition & Finding.

Choose a one- or two-tailed test for Z- and t-scores based on your hypothesis. The default two-tailed option is most common and tests for deviations in both directions. Learn more in my post: One- and Two-Tailed Tests Explained.

Only Right-Tailed Critical Values for Chi-Square and F Tests

This critical value calculator reports only right-tailed critical values for chi-square and F distributions. That’s because these tests measure magnitude—not direction—and the distributions are bounded at zero and skewed to the right. You can’t have negative chi-square or F values, and the concept of a “left tail” doesn’t apply.

In a chi-square test, you sum squared differences between observed and expected counts. In an F-test, you calculate the ratio of sample variances. Both procedures assess whether the test statistic exceeds a critical threshold, making them fundamentally right-tailed tests. Smaller values suggest better fit or lower variance but don’t contradict the null hypothesis. The only area of concern lies in the right tail, which this calculator uses to determine statistical significance.