Chi-Square p-Value Calculator
Use this tool to calculate the right-tail p-value from a chi-square statistic and degrees of freedom.
Note: For chi-square tests, the p-value is typically the upper-tail probability: P(X ≥ χ²).
What this calculator does
A chi-square test gives you a test statistic (χ²). To decide whether your result is statistically significant, you need the p-value. This calculator converts your chi-square statistic and degrees of freedom into a p-value instantly.
It is useful for common procedures like:
- Chi-square goodness-of-fit test
- Chi-square test of independence (contingency tables)
- Chi-square test of homogeneity
How to calculate p-value from chi-square
The p-value for a chi-square test is the area in the right tail of the chi-square distribution beyond your observed statistic. In notation:
p-value = P(Χ²df ≥ χ²observed)
Where:
- χ²observed is your computed test statistic
- df is the degrees of freedom
- Χ²df is a chi-square random variable with df degrees of freedom
Under the hood, this uses the regularized incomplete gamma function, which is the standard numerical method used in statistical software.
Step-by-step example
Example values
- Chi-square statistic: χ² = 10.83
- Degrees of freedom: df = 4
- Significance level: α = 0.05
Enter these values in the calculator. You’ll get a p-value around 0.0285. Because 0.0285 is less than 0.05, you reject the null hypothesis at the 5% significance level.
Interpreting the result
General interpretation guide
- p < α: statistically significant; reject H₀.
- p ≥ α: not statistically significant; fail to reject H₀.
A small p-value means your observed data would be unlikely if the null hypothesis were true. It does not measure effect size or practical importance.
Common degrees of freedom formulas
Goodness-of-fit test
df = k - 1 - m, where k is number of categories and m is number of estimated parameters.
Test of independence / homogeneity
df = (r - 1)(c - 1), where r is rows and c is columns in your contingency table.
Mistakes to avoid
- Using the wrong degrees of freedom formula.
- Treating p-value as proof that the alternative hypothesis is true.
- Ignoring assumptions, such as expected counts being sufficiently large.
- Reporting significance without context, confidence intervals, or effect size.
Quick FAQ
Is this a one-tailed or two-tailed p-value?
For chi-square tests, it is normally a right-tailed probability. So this calculator returns the right-tail p-value.
Can degrees of freedom be non-integer?
In most introductory chi-square tests, df is an integer. Numerically, the distribution is defined for any positive df, and this calculator supports positive values.
What if p-value is extremely small?
Extremely small p-values may display in scientific notation (for example, 2.1e-8), which still indicates strong evidence against the null hypothesis.