Chi-Squared Distribution Calculator
Compute chi-squared probabilities, critical values, and p-values for goodness-of-fit and independence tests with interactive charts.
The chi-squared distribution arises naturally as the sum of squared standard normal variables. It is the foundation for goodness-of-fit tests, tests of independence in contingency tables, and confidence intervals for variance.
This calculator lets you evaluate tail probabilities, find critical values for a given significance level, and explore how degrees of freedom shape the distribution from highly skewed to nearly symmetric.
Launch the Chi-Squared Distribution workspace to plot the curve, inspect PDF/CDF behavior, and compute quantiles and interval probabilities.
Open Interactive Interval ProbabilityWhen do I use a chi-squared test?
Use it for goodness-of-fit tests (comparing observed vs expected frequencies), tests of independence in contingency tables, and confidence intervals for population variance.
How do I find the chi-squared critical value?
Set the quantile to 1 − α (for example, 0.95 for a 5% significance level) with your degrees of freedom and read the critical value.
Why is the chi-squared distribution always positive?
Because it is defined as a sum of squared values, which are always non-negative. The distribution is supported on [0, ∞).