How do you calculate the p value for a chi-square test?

The p value is the area in the right tail of the chi-square distribution beyond your test statistic, at your degrees of freedom. You need two inputs: the chi-square value and df. A table gives you a range. This calculator returns the exact value.

What p value counts as significant for a chi-square test?

Most fields use .05 as the threshold. A p value below .05 means the observed pattern would be unlikely if the variables were unrelated. The threshold is a convention, not a property of the data.

What are the degrees of freedom for a chi-square test?

For a test of independence, df equals (rows minus 1) times (columns minus 1). For a goodness of fit test, df equals the number of categories minus 1.

Why does my chi-square p value say the result is unreliable?

The chi-square p value is an approximation that breaks down when expected cell counts are small. If more than 20 percent of expected counts fall below 5, consider Fisher's exact test or combine categories.

Chi-Square Test Calculator with Exact P Value

How to calculate the p value for a chi-square test

The p value is the area in the right tail of the chi-square distribution that sits beyond your test statistic, at your degrees of freedom. Two inputs produce it: the chi-square value and df. Nothing else.

Degrees of freedom come from the shape of the data, not the sample size. For a test of independence, df = (rows − 1) × (columns − 1). For goodness of fit, df = number of categories − 1.

Worked example

Take a 2×2 table of 85 people: 30 and 12 in the first row, 18 and 25 in the second.

Row totals are 42 and 43. Column totals are 48 and 37. N = 85.
Each expected count is (row total × column total) ÷ N. The first cell expects 42 × 48 ÷ 85 = 23.72.
For every cell, square the gap between observed and expected, then divide by expected. Add the four results: χ² = 7.56.
df = (2 − 1) × (2 − 1) = 1.
A chi-square of 7.56 at df = 1 gives p = .006. Below .05, so the association is statistically significant.

Run those same numbers through the calculator above and you get χ²(1, N = 85) = 7.56, p = .006, φ = .30.

Chi-square to p value reference table

Critical values below. If your chi-square statistic is larger than the value in a column, your p value is smaller than that column's threshold. A table gives you a range; the calculator gives you the exact number.

df	p = .05	p = .01	p = .001
1	3.841	6.635	10.828
2	5.991	9.210	13.816
3	7.815	11.345	16.266
4	9.488	13.277	18.467
5	11.070	15.086	20.515
6	12.592	16.812	22.458
7	14.067	18.475	24.322
8	15.507	20.090	26.124
9	16.919	21.666	27.877
10	18.307	23.209	29.588

Worked from the chi-square distribution, upper tail. Reporting an exact p value is the APA 7 preference; use the table to sanity check, not to report.

Which chi-square test do I need?

Test of independence: two categorical variables, one sample. Example: is program completion (yes/no) related to enrollment status (full time/part time)? Enter the cross-tabulated counts.

Goodness of fit: one categorical variable compared against expected proportions. Example: do students choose the four majors equally often? Enter observed counts and, if the expectation is not equal shares, the expected proportions.

When the p value is not trustworthy

Counts must be frequencies of independent observations, not percentages and not repeated measures of the same people.
Expected counts should generally be 5 or more in at least 80% of cells. The calculator warns you when they are not; with small 2×2 tables, consider Fisher's exact test.
The chi-square p value is an approximation. With sparse tables it drifts, and a borderline p near .05 can flip once you switch to an exact test.

Effect size

A small p value tells you the association is unlikely to be chance. It does not tell you the association is large. For tests of independence the calculator reports Cramer's V (phi for 2×2 tables). Values around .10 are small, .30 medium, and .50 large for df* = 1, with thresholds shrinking as tables grow.

Report both. A p of .001 with a V of .08 is a real but trivial association, and the p value alone hides that.

Related calculators

Correlation calculator for two continuous variables (Pearson r, Spearman rho, and p value)
Independent samples t test for comparing two group means
Cohen's d calculator for effect size on mean differences
Which statistical test should I use? if you are not sure chi-square is the right choice

A chi-square result gets harder to defend when expected counts are small, when the table is bigger than two by two, or when the same people appear in more than one cell. If you are unsure whether the test holds up in your design, a written review by a PhD statistician costs less than finding out at peer review.