Chi Square Calculator
Goodness of fit test statistic.
Reviewed by the Calculation Machine team · How we check our maths
Your values
ⓘ Live results
Results
- Chi square statistic
- 37.818
- Degrees of freedom
- 5
- Critical value at 0.05
- 11.07
- Result
- Reject the null hypothesis
| Category | Observed | Expected | (O−E)²/E |
|---|---|---|---|
| 1 | 30 | 33.3 | 0.327 |
| 2 | 14 | 33.3 | 11.1859 |
| 3 | 34 | 33.3 | 0.0147 |
| 4 | 45 | 33.3 | 4.1108 |
| 5 | 57 | 33.3 | 16.8676 |
| 6 | 20 | 33.3 | 5.312 |
Quick answer
Chi square sums the squared difference between observed and expected counts, divided by expected, across all categories.
The formula
χ² = Σ (O − E)² / E
Worked example
Worked example
Using the values the calculator loads with.
Inputs
- Observed counts30, 14, 34, 45, 57, 20
- Expected counts33.3, 33.3, 33.3, 33.3, 33.3, 33.3
Result
- Chi square statistic37.818
- Degrees of freedom5
- Critical value at 0.0511.07
- ResultReject the null hypothesis
How to use the Chi Square Calculator
- 1Enter observed counts separated by commas.
- 2Enter the matching expected counts.
- 3Compare the statistic to the critical value.
Frequently asked questions
What if expected counts are small?
Chi square is unreliable when expected counts fall below 5 — combine categories.
Is this the same as a test of independence?
The formula is identical; only the degrees of freedom differ.
About this calculator
- Built and reviewed by the Calculation Machine team · How we build and test calculators
- Report an error