What the tool does, how to run it, and what to expect from the result.
χ² = Σ (observed − expected)² ÷ expected. Goodness of fit compares one row of counts with expected counts: a die rolled 120 times landing 22, 17, 20, 26, 22, 13 gives χ² = 5.1 with 5 degrees of freedom, p = 0.404, no evidence the die is unfair. For independence, expected = row total × column total ÷ grand total: the table 20, 30 / 30, 20 gives χ² = 4, df = 1, p = 0.0455, significant at 0.05.
A quick way to understand who this helps, what it solves, and where it connects next.
Students, teachers, analysts and researchers working with data.
Using the chi-square calculator without installing anything or signing up.
Short answers for the questions people usually have before trying a utility like this.
The probability of a χ² this large if the null hypothesis (fair die, or no association) were true. Below 0.05 is the usual cut-off for significance.
When expected counts are small (a common rule: any below 5). The calculator warns you; use Fisher’s exact test for small 2 × 2 tables.
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Expected counts: 20, 20, 20, 20, 20, 20
All expected counts are 5 or more, so the chi-square approximation is reasonable.