0.047266
0.952734
0.094532
1.67196
0.047266
0.952734
0.094532
1.67196
This Chi-Square (X²) P-Value Calculator converts a chi-square statistic into a p-value using a fast, practical approximation. It’s commonly used for goodness-of-fit tests and tests of independence in contingency tables.
Enter your X²-score and degrees of freedom (df). The calculator returns the right-tailed p-value (the most common interpretation for chi-square tests), along with left-tailed and two-tailed values for reference.
For chi-square tests, p-values come from the chi-square distribution, which depends on df. In most chi-square hypothesis tests, the p-value is computed as the right-tail probability:
This calculator uses the Wilson–Hilferty transform to map the chi-square statistic to a z-like value and then estimates tail probabilities via the standard normal CDF.
Right-tailed p-value is typically the one reported in chi-square tests (goodness-of-fit and independence). A smaller right-tailed p-value means your observed chi-square statistic is more extreme under the null hypothesis.
Many U.S. use cases compare the p-value to 0.05, but always interpret results alongside effect size, sample size, and context.
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X² ≈ 3.84 with df = 1 is a classic cutoff near p ≈ 0.05 (right tail).
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X² ≈ 5.99 with df = 2 is near p ≈ 0.05 (right tail).
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A larger chi-square statistic pushes further into the right tail; p gets smaller.
In most chi-square tests (goodness-of-fit and independence), you report the right-tailed p-value: the probability of getting a chi-square statistic at least as large as the observed value under the null hypothesis.
df depends on the test. For goodness-of-fit, it’s often (number of categories − 1 − estimated parameters). For independence in an r×c table, df is typically (r − 1)(c − 1).
The chi-square statistic is a sum of squared terms, so it cannot be negative. This calculator treats negative entries as 0 for stability.
This version uses a fast approximation (Wilson–Hilferty). It’s usually very close for practical df values. Exact matching would require the chi-square CDF (incomplete gamma) in the backend math engine.
Not always. With large samples, even small differences can produce tiny p-values. Consider effect size measures (like Cramér’s V) and context.
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