Free interactive student tool
Free Chi-Square Calculator
Free Chi-Square Calculator. Goodness-of-fit and independence modes with expected-count checks.
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Σ (observed − expected)² ÷ expected
How this tool reaches its result
The chi-square statistic accumulates standardized discrepancies between observed and expected counts.
Σ (observed − expected)² ÷ expected
Worked context
How to interpret the output
A 2 × 2 table has one degree of freedom. Expected counts are calculated from the row and column totals.
Important limitation
What the result cannot decide for you
Small expected counts may require an exact test or category consolidation.