Chi-Square Calculator — Goodness of Fit Test (Free)

Use this free chi-square calculator to run a goodness-of-fit test. Enter the observed counts and the expected counts (or leave expected blank for equal categories), and you’ll get the χ² statistic, the degrees of freedom, the p-value, and each category’s contribution.

How to use the calculator

1. Enter the observed counts, separated by commas.
2. Enter the expected counts (or leave blank to assume equal categories).
3. Read the χ² statistic, degrees of freedom, and p-value.

The chi-square statistic

The test compares observed to expected counts with χ² = Σ (O − E)² / E. The degrees of freedom are k − 1 for k categories, and the p-value tells you how surprising the result is if the expected model were true.

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Frequently asked questions

What does the chi-square test do?

It measures how far observed counts are from expected counts. A large χ² (and small p-value) suggests the data don’t fit the expected model.

How many degrees of freedom?

For a goodness-of-fit test with k categories, df = k − 1.

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What is the p-value?

The probability of a χ² at least as large as the one observed if the expected model is correct. Small p-values (e.g. < 0.05) cast doubt on that model.

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Read the full lesson: learn the method step by step.

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