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 is the chance of a gap at least this large if the null hypothesis, that the counts follow the expected pattern, is true.

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.

What is the chi-square critical value at 0.05?

This calculator reports a p-value, which you compare with α, instead of a critical value. If you work from a table, the 0.05 critical values are 3.841 for 1 df, 5.991 for 2 df, 7.815 for 3 df, 9.488 for 4 df and 11.070 for 5 df. A χ² above the critical value is the same result as a p-value below 0.05.

Can I enter expected percentages or a ratio like 9:3:3:1?

Enter expected counts, not percentages. The calculator uses each Expected value exactly as typed and does not rescale it to your total, so convert first: expected count = total observed × proportion. For 556 seeds and a 9:3:3:1 ratio that is 312.75, 104.25, 104.25 and 34.75. Leave every Expected cell blank to test for an equal split.

Chi Square Calculator

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

χ² = Σ (O − E)² ÷ E, added up over every cell.

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

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Degrees of Freedom

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P-Value

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Cell Breakdown

Cell	Observed	Expected	(O−E)²/E

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Quick answer

χ² = Σ (O − E)² ÷ E, added up over every cell. Degrees of freedom are categories − 1 for a goodness-of-fit test and (rows − 1) × (columns − 1) for a contingency table, and the p-value is the upper-tail chi-square probability. Getting 60 heads in 100 coin flips gives χ² = 4.0000 with 1 df and p = 0.0455, which is significant at 0.05.

Examples

Observed	χ² (df)	p-value
Coin 60, 40	4.0000 (1)	0.0455
Die 8,9,12,11,6,14	4.2000 (5)	0.5210
Die 30,10,10,10,10,20	23.3333 (5)	0.0003
Mendel 9:3:3:1	0.4700 (3)	0.9254
2×2: 20,30/30,20	4.0000 (1)	0.0455
2×3: 10,20,30/20,20,20	5.3333 (2)	0.0695

Enter your observed counts and click Calculate χ².

Summary

This chi-square calculator computes the χ² statistic and its associated p-value from your observed and expected frequency counts. It supports both goodness-of-fit tests (one row of categories) and contingency-table independence tests (multiple rows and columns). Click Calculate to update the results and see a clear interpretation of statistical significance.

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: 2026-06-04 · Reviewed by Nham Vu