Chi-Square Goodness of Fit Calculator
Checks whether counts fit a pattern you specified in advance, such as whether a die is fair.
p-value
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
Values read in each list —
Chi-square —
Degrees of freedom —
Critical value —
Reading this —
The formula
χ² = Σ (observed − expected)² ÷ expected df = categories − 1
Expected values are scaled so they add up to the observed total.
What to watch out for
For two categorical variables in a table, use the test of independence instead.
Frequently Asked Questions
How would I test a die?
Enter the count of each face and leave the expected list blank. Counts of 16, 18, 16, 14, 12, 12 give χ² = 2 and p = 0.84915, which is no evidence of bias.
Can I enter a ratio like 9:3:3:1?
Yes. Enter 9, 3, 3, 1 as the expected list, and it is scaled to your total.