chi square p calculator

Chi-Square P-Value Calculator

Enter a chi-square statistic (χ²) and degrees of freedom (df) to compute the right-tail p-value used in most chi-square tests.

Enter values and click Calculate p-value.

This tool returns the upper-tail probability: p = P(X ≥ χ²) for X ~ χ²(df).

What this chi square p calculator does

This calculator helps you convert a computed chi-square test statistic into a p-value. In practical terms, it tells you how surprising your observed statistic would be if the null hypothesis were true.

It works for common use cases such as:

Chi-square test of independence (contingency tables)
Chi-square goodness-of-fit tests
Variance-related tests that map to the chi-square distribution

How to use it

Run your chi-square test and record the test statistic (χ²).
Determine the degrees of freedom (df).
Enter both values in the calculator.
Optionally set your significance level, usually 0.05.
Click Calculate p-value.

You will get:

Right-tail p-value
Lower-tail cumulative probability
A quick significance decision based on your chosen α

Formula behind the calculator

For a chi-square statistic x with k degrees of freedom:

p-value (right-tail) = P(X ≥ x), where X ~ χ²(k) Equivalent form: p = Q(k/2, x/2) Q(·,·) is the regularized upper incomplete gamma function.

The script on this page computes that value numerically using stable gamma-function approximations (series and continued fraction methods).

Degrees of freedom: quick reference

Test type	Degrees of freedom (df)
Goodness-of-fit	Number of categories - 1 - estimated parameters
Independence / homogeneity (r x c table)	(r - 1)(c - 1)
Single variance test (normal population)	n - 1

Worked example

Suppose your test gives χ² = 10.83 and df = 4. Enter those values into the calculator.

The p-value is about 0.0285 (approximately, depending on rounding), which is less than 0.05. That means your result is statistically significant at the 5% level, so you would reject the null hypothesis.

How to interpret your p-value

p < α: evidence against the null hypothesis (statistically significant).
p ≥ α: insufficient evidence to reject the null hypothesis.

A p-value does not tell you effect size, practical importance, or the probability that the null is true. It is only a compatibility measure between your data and the null model.

Common mistakes to avoid

1) Using the wrong degrees of freedom

This is the most common error. Double-check formulas for your specific test design.

2) Mixing up tails

Standard chi-square tests for independence and goodness-of-fit are right-tailed. This calculator is designed for that use.

3) Interpreting non-significant as “proof of no effect”

A large p-value means your data do not provide strong evidence against the null; it does not prove the null hypothesis.

FAQ

Can I enter decimal chi-square values?

Yes. The statistic can be any non-negative real number.

Must df be an integer?

In classical chi-square tests, yes. This calculator expects a positive integer df.

What if p is extremely small?

The calculator will display scientific notation for very small p-values.