Chi-Square to P-value Calculator
Why convert chi-square to a p-value
A chi-square statistic alone has no fixed meaning: bigger hints at trouble, but nothing marks the line. This Chi-Square to P-value Calculator turns the statistic into a p-value, the probability of a result at least this extreme when the null hypothesis is true. It follows goodness of fit tests, independence tests on contingency tables, and variance comparisons.
The method behind the conversion
The p-value is the area to the right of your statistic under the chi-square curve with your degrees of freedom, so p = 1 minus CDF(x, df). For example, a statistic of 10 with df = 2 gives an upper tail of e^(-5), about 0.0067. A statistic of 3.84 with df = 1 lands almost exactly at 0.05.
Using the calculator in three steps
Enter the Chi Square statistic from your test output, then enter the matching Degrees of freedom, often (rows minus 1) times (columns minus 1) for independence tests. Press Calculate P-value and read the result. Below 0.05 is conventionally significant, below 0.01 strongly so. Double-check the degrees of freedom first, since small errors there shift the p-value dramatically.
A die fairness check shows the inputs in action. Roll a die 600 times; each face expects 100. Counts of 124, 82, 101, 96, 113, and 84 give a Chi Square statistic of 13.42. With 5 Degrees of freedom (six faces minus 1), press Calculate P-value and you get about 0.02, strong evidence the die is biased. The same 13.42 with 10 degrees of freedom would sit near p = 0.20, harmless, which is why the second field is never optional.
Frequently Asked Questions
Can a chi-square statistic be negative?
No. The statistic is built from squared terms, so every contribution is zero or positive. Its smallest value is 0, which corresponds to a p-value of 1, a perfect fit.
What counts as a significant p-value?
By convention, p below 0.05 is significant and below 0.01 is strong evidence. Report the exact number rather than only the verdict, since 0.05 is a threshold, not a law.
What does degrees of freedom mean?
It counts how many independent values feed the statistic. For a contingency table it equals (rows minus 1) times (columns minus 1); goodness of fit tests usually use categories minus 1.
Is this p-value one or two tailed?
One upper tail. Only large positive chi-square values signal departure from expectation, so the whole rejection region sits in the right tail and the area is never doubled.
Does a larger statistic lower the p-value?
Yes, at fixed degrees of freedom. A statistic of 15 with df = 1 gives about p = 0.0001, so larger gaps from expected frequencies mean stronger evidence.