Chi-Square Goodness of Fit Calculator
Compare observed vs expected category counts.
Enter your values
ⓘ Live results
Results
- Chi-square statistic
- 2.9
- Degrees of freedom
- 3
- Categories
- 4
Quick answer
The chi-square statistic sums the squared difference between observed and expected counts, divided by expected, across all categories.
χ² = Σ (O-E)²/E
How to use the Chi-Square Goodness of Fit Calculator
- 1List the observed count for each category.
- 2List the expected count for each matching category.
- 3The chi-square statistic sums the squared relative differences; compare it to a chi-square table with df = categories - 1.
Worked example
Using the values the calculator loads with:
Inputs
- Observed counts (comma-separated)18,22,25,15
- Expected counts (comma-separated)20,20,20,20
Results
- Chi-square statistic2.9
- Degrees of freedom3
- Categories4
Frequently asked questions
What counts as a good fit?
A small chi-square statistic relative to the degrees of freedom suggests observed data matches expected well.
What if expected counts are very small?
The chi-square approximation works best when expected counts are at least 5 per category.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.