Statistics

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.

Results
Chi square statistic
37.818
Degrees of freedom
5
Critical value at 0.05
11.07
Result
Reject the null hypothesis
CategoryObservedExpected(O−E)²/E
13033.30.327
21433.311.1859
33433.30.0147
44533.34.1108
55733.316.8676
62033.35.312

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 doesGoodness of fit test statistic.
CategoryStatistics
Inputs neededObserved counts, Expected counts
Main outputChi square statistic
Formulaχ² = Σ (O − E)² / E
CostFree — no sign-up, no download

How to use the Chi Square Calculator

  1. 1Enter observed counts separated by commas.
  2. 2Enter the matching expected counts.
  3. 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.