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.
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.
For multiple categories, total χ² is the sum of (O - E)² ÷ E across all categories.
So the chi square value for this observed vs expected pair is 2.
Subtract, square, then divide by expected.
How to Use the Chi-Square Calculator
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Enter the observed value (O).
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Enter the expected value (E).
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The calculator applies χ² = (O - E)² ÷ E.
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If you have multiple categories, calculate each term and add them together.
Frequently Asked Questions
For one observed/expected pair: χ² = (O - E)² ÷ E. For multiple categories, sum that value across categories.
No. Chi square is based on a squared difference, so χ² is always 0 or positive.
It’s a statistic that measures how far observed results deviate from expected results under a hypothesis, commonly used in chi-square tests.
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?).
Yes—this chi-square calculator online computes χ² from observed and expected values using the chi square formula.
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.
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.
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).
χ² is the standard symbol for the chi-square statistic.
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.