What is the chi-square test?

The chi-square (χ²) test is a statistical test that measures how well observed data matches expected data. A large χ² value means the observed and expected counts differ greatly. The p-value tells you the probability of seeing that difference by chance.

What does the p-value mean?

The p-value is the probability of obtaining a χ² value at least as extreme as the one computed, assuming the null hypothesis is true. A p-value below your significance level (typically 0.05) indicates statistical significance — meaning the deviation from expectation is unlikely due to random chance.

How are degrees of freedom calculated?

For goodness-of-fit, df = (number of categories − 1). For an independence test on an r × c contingency table, df = (r − 1) × (c − 1).

What sample size is needed for the chi-square test?

Each expected cell count should generally be at least 5. If any expected count is below 5, results may be unreliable and Fisher's exact test is often preferred instead.

Can I use this for a two-way contingency table?

Yes. Switch to Independence mode, set the number of rows and columns, then enter your observed counts. Expected values are automatically calculated from row and column marginal totals.

Chi Square Calculator

Enter observed and expected counts to instantly compute the chi-square statistic, degrees of freedom, and p-value.

Test Configuration

Test Type

Number of Categories

Leave Expected blank to assume equal distribution.

Significance Level (α)

Enter your data and click Calculate to see results.

χ² Statistic

—

Degrees of Freedom

—

P-Value

—

Cell Breakdown

Cell	Observed	Expected	(O−E)²/E

Copied!

Summary

Enter observed and expected counts to instantly compute the chi-square statistic, degrees of freedom, and p-value.

How it works

Choose between Goodness-of-Fit or Independence (contingency table) mode.
Enter the number of categories or table dimensions.
Fill in your observed counts (and expected counts for goodness-of-fit).
The calculator computes χ² = Σ (O − E)² / E across all cells.
Degrees of freedom are calculated automatically from your table size.
The p-value is derived from the chi-square cumulative distribution function.

Use cases

Test whether a die is fair by comparing rolled outcomes to expected uniform distribution.
Analyze survey responses to check if preferences differ by demographic group.
Validate genetics experiments against expected Mendelian ratios.
Check whether website conversion rates are independent of traffic source.
Assess whether observed frequency data fits a theoretical distribution.
Quality-control checks on manufacturing defect rates across production lines.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu