Chi-Square Distribution Calculator

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Chi-Square Distribution Calculator

Use this chi-square distribution calculator to turn a χ² statistic into a p-value, or to find the critical χ² value for a given significance level and degrees of freedom. The chi-square distribution is right-skewed, starts at zero and has mean equal to its df; it is the reference distribution for the goodness-of-fit and independence tests and for confidence intervals on a variance.

In probability mode, enter the statistic and df and choose the tail. Chi-square tests are right-tailed, so P(χ² ≥ x) is the usual p-value; the left tail and two-tailed options cover variance intervals and other uses. In critical value mode, enter α and the tail to get the cut-off, for example 9.488 for α = 0.05 with 4 df.

The plot shades the region measured. Values are computed from the regularised incomplete gamma function, so they agree with R, SciPy and Excel’s CHISQ.DIST to many decimal places. See the chi-square table for a printable version and the test of independence to run a full test.

Frequently asked questions

How do I find the p-value for a chi-square test?

Choose probability mode, enter the χ² statistic and df, and select the right tail. The p-value is P(χ² ≥ statistic).

What is the critical chi-square value at 0.05 with 1 df?

3.841. With 2 df it is 5.991, with 3 df 7.815 and with 10 df 18.307.

Why is the chi-square test one-tailed?

Because any difference between observed and expected counts, positive or negative, increases the statistic. Only large values are evidence against H₀.

What are the mean and variance of the chi-square distribution?

Mean = df and variance = 2 × df. The distribution becomes approximately normal for large df.

Last reviewed: September 25, 2026. Calculations run in your browser and were validated against SciPy.