Chi Square Calculator
Goodness of fit test statistic.
Enter your values
Enter the observed counts you are working with.
Enter the expected counts you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
χ² = Σ (O − E)² / E
At a glance
| What it does | Goodness of fit test statistic. |
|---|---|
| Category | Statistics |
| Inputs needed | Observed counts, Expected counts |
| Main output | Chi square statistic |
| Formula | χ² = Σ (O − E)² / E |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Observed counts
- Enter the observed counts you are working with.
- Expected counts
- Enter the expected counts you are working with.
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
Results
- Chi square statistic37.818
- Degrees of freedom5
- Critical value at 0.0511.07
- ResultReject the null hypothesis
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.
What do I need to enter into the Chi Square Calculator?
Just 2 values: observed counts, expected counts. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Chi Square Calculator work out the answer?
Chi square sums the squared difference between observed and expected counts, divided by expected, across all categories. It applies the formula χ² = Σ (O − E)² / E and shows the working so you can check each step by hand.
Is the Chi Square Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.