Chi-Square Calculator

Use our chi-square calculator to calculate chi square (χ²) instantly from observed and expected values. Includes the chi square formula, chi square example, and a simple explanation of chi square in statistics—plus notes on chi square tables, charts, and when chi square should be used.

Observed value (O)
Enter the observed frequency.
Expected value (E)
Enter the expected frequency.
Results
Chi-Square (χ²)
Calculated as (O − E)² ÷ E.
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What is Chi-Square (χ²)?

Chi-square (also written chi square or χ²) is a statistic used to measure how different observed data is from what you would expect under a hypothesis. It’s a core tool for chi square analysis in statistics.

You’ll see chi square in statistics most often in chi-square tests, like goodness-of-fit tests and tests of independence. A chi square calculator helps you compute the chi square statistic quickly.

This page is a simple chi-square calculator online for one observed value and one expected value. (Many full chi square statistic calculators sum χ² across multiple categories, but each term uses the same chi square formula.)

Chi-Square Formula

To calculate chi square for a single observed/expected pair, subtract expected from observed, square the result, then divide by expected.

Chi-square (single term) =
χ² = (O - E)² ÷ E

For multiple categories, total χ² is the sum of (O - E)² ÷ E across all categories.

χ²
= Chi-square statistic (chi square symbol)
O
= Observed value
E
= Expected value
Chi square example
O=60, E=50 → χ² = (60-50)² ÷ 50 = 100 ÷ 50 = 2

So the chi square value for this observed vs expected pair is 2.

Chi square on calculator (quick steps)
(O − E) → square → ÷ E

Subtract, square, then divide by expected.

How to Use the Chi-Square Calculator

  1. 1

    Enter the observed value (O).

  2. 2

    Enter the expected value (E).

  3. 3

    The calculator applies χ² = (O - E)² ÷ E.

  4. 4

    If you have multiple categories, calculate each term and add them together.

Frequently Asked Questions

How do I calculate chi square?

For one observed/expected pair: χ² = (O - E)² ÷ E. For multiple categories, sum that value across categories.

Can chi square be negative?

No. Chi square is based on a squared difference, so χ² is always 0 or positive.

What is chi square in statistics?

It’s a statistic that measures how far observed results deviate from expected results under a hypothesis, commonly used in chi-square tests.

When should chi square be used?

Chi-square tests are typically used with categorical/count data—for goodness-of-fit (does data match a distribution?) or independence (are two categorical variables related?).

Is this a chi-square calculator / chi square calculator online?

Yes—this chi-square calculator online computes χ² from observed and expected values using the chi square formula.

What is a chi square chart / chi square table?

A chi square table (or chi square chart) lists critical values of the chi-square distribution by degrees of freedom and significance level. It’s used to compare your χ² statistic to determine significance.

What is a chi square distribution calculator?

A chi square distribution calculator uses degrees of freedom to compute probabilities, p-values, or critical values from the chi-square distribution. This page focuses on computing the χ² statistic term from observed vs expected.

What is the chi square function?

In many tools, “chi square function” refers to functions that compute chi-square distribution probabilities or inverse critical values. The core statistic still uses χ² = Σ((O - E)² ÷ E).

What does χ² (chi square symbol) mean?

χ² is the standard symbol for the chi-square statistic.

Is chi square capitalized?

Both “chi-square” and “Chi-square” are used in writing. In titles, it’s often capitalized as “Chi-Square.” The symbol χ² is not capitalized.

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