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Chi-Square Calculator

Compute the chi-square goodness-of-fit statistic.

Introduction

Chi-Square Calculator — Compute the chi-square goodness-of-fit statistic. Enter Observed values (comma-separated), Expected values (comma-separated) to get an instant, accurate result.

Formula

Goodness-of-fit statistic: χ² = Σ((observed − expected)² / expected), summed across all categories; degrees of freedom = number of categories − 1.

Step-by-step

  1. Enter the Observed values (comma-separated).
  2. Enter the Expected values (comma-separated).
  3. Click Calculate to see your result instantly.

Real-world example

Example: With Observed values (comma-separated) = 10, 20, 30, 40, Expected values (comma-separated) = 20, 20, 20, 40, the Chi-Square Calculator gives Chi Square: 10, Degrees Of Freedom: 3.

Frequently Asked Questions

What does the chi-square statistic tell you?
A larger χ² indicates a bigger discrepancy between your observed data and the expected/theoretical distribution; it's compared against a chi-square distribution to get a p-value.
What happens if an expected value is zero?
That category is skipped in the sum, since dividing by an expected value of zero is undefined — an expected frequency of zero also violates the test's assumptions.
What inputs does the Chi-Square Calculator need?
You'll need to provide: Observed values (comma-separated), Expected values (comma-separated). All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Chi-Square Calculator?
The Chi-Square Calculator applies the formula exactly as calculated — Goodness-of-fit statistic: χ² = Σ((observed − expected)² / expected), summed across all categories; degrees of freedom = number of categories − 1. — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Chi-Square Calculator free to use?
Yes, the Chi-Square Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Chi-Square Calculator

The Chi-Square Calculator uses a real, verifiable formula — Goodness-of-fit statistic: χ² = Σ((observed − expected)² / expected), summed across all categories; degrees of freedom = number of categories − 1. — so results are accurate every time, not an approximation.