What is a chi-square calculator?
A chi-square goodness-of-fit test compares observed category counts with counts expected under a stated model. Larger discrepancies produce a larger statistic and typically a smaller upper-tail p-value.
Use this page for a transparent calculation, then compare the result with the Probability Calculator when a different view of the same data would be useful.
How does this chi-square calculator work?
The calculator sums each squared observed-minus-expected difference divided by its expected count, uses k − 1 degrees of freedom, and evaluates the chi-square upper tail.
Before interpreting spread or position, it can help to check the center with the Sample Size Calculator. Every tool states its assumptions so results can be reproduced.
How to use this calculator
- Enter the requested numbers in the labeled fields.
- Review unit, sample, confidence, or test choices when shown.
- Select Calculate Chi-Square.
- Read the main result, supporting facts, and method note.
- Use Copy, Download, or Print when you need to keep the result; select Reset to start over.
If you edit any input after calculating, the old result is marked stale and hidden until you calculate again.
How should you interpret the result?
A p-value below the chosen α indicates the observed pattern would be relatively unusual under the expected model. Failing to reject does not prove the model is true.
For another useful perspective, open the Confidence Interval Calculator; it answers a related question without changing the values you entered here.
Assumptions and limitations
Expected counts must be set appropriately, categories must be independent and mutually exclusive, and small expected counts can make the approximation unreliable.
Consider the Correlation Calculator for a complementary summary and the Percentile Calculator when your question involves another statistical property. No single statistic describes every important feature of a data set.
Frequently asked questions
Sources and methodology
The formulas and cautions on this page are documented so the calculation can be checked against authoritative statistical guidance.