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Chi-square distribution calculator

The chi-square distribution calculator returns tail probabilities and critical values for χ² on a given number of degrees of freedom.

What is Chi-square distribution calculator?

Chi-square is the distribution of a sum of squared standard normals, which is why it appears in goodness-of-fit tests, tests of independence in a contingency table, and inference about a variance.

Chi-square is skewed and its shape changes with df, so the upper and lower tails are not mirror images — the calculator reports each separately rather than assuming symmetry.

When should I use Chi-square distribution calculator?

Converting a χ² statistic from a contingency table into a p-value.
Finding the critical value for a goodness-of-fit test.
Building a confidence interval for a variance.

What data does it need?

Distribution parameters, plus a value x, a tail probability p, or both.

What does it report?

For x: the density or exact probability and each tail. For p: the lower, upper and two-tailed critical values.

What does it assume?

None — this evaluates a distribution rather than testing data against one.