🎲 Chi-Square Test Calculator
Enter observed and expected counts (goodness-of-fit) or a contingency table (independence) to get the χ² statistic, df, p-value and verdict.
χ² statistic
1
Degrees of freedom
5
p-value
0.9626
Not significant at α = 0.05
p = 0.9626 ≥ 0.05: the observed counts are consistent with the expected distribution.
The chi-square test compares observed counts to what a hypothesis predicts: χ² = Σ (O − E)² ÷ E. Goodness-of-fit checks whether one categorical variable follows an expected distribution (df = categories − 1); the independence test checks whether two variables in a contingency table are related (df = (rows − 1)(cols − 1), with expected counts from the row and column totals). It needs counts, not percentages, and expected counts should generally be 5 or more. 🔒 In your browser.
How the chi-square test calculator works
The chi-square test compares observed counts with the counts a hypothesis predicts: χ² = Σ (observed − expected)² ÷ expected. In goodness-of-fit mode you supply observed and expected counts for one categorical variable (df = categories − 1). In independence mode you paste a contingency table and the tool derives the expected counts from the row and column totals, testing whether the two variables are related (df = (rows − 1)(columns − 1)). It converts χ² to an exact p-value.
The test needs raw counts, not percentages, and the usual rule of thumb is that expected counts should be at least 5 in each cell for the approximation to hold. A significant result (p below α) means the observed pattern departs from the hypothesis, a poor fit, or an association between the variables, but chi-square shows that a relationship exists, not how strong it is or which direction.
Frequently asked questions
How do I calculate a chi-square test?
For each category or cell, take (observed − expected)², divide by expected, and sum: χ² = Σ (O − E)² ÷ E. Then find the degrees of freedom and convert χ² to a p-value using the chi-square distribution. The tool does all of this from your counts.
What is the difference between goodness-of-fit and independence?
Goodness-of-fit tests whether one categorical variable matches an expected distribution (e.g. is a die fair?). The test of independence uses a two-way table to check whether two categorical variables are associated (e.g. is preference related to age group?).
How are the expected counts found in a test of independence?
For each cell, expected = (its row total × its column total) ÷ grand total, the count you'd see if the two variables were completely independent. The tool computes and can display the full expected table.
What are the degrees of freedom for a chi-square test?
For goodness-of-fit, categories − 1. For a test of independence on an r×c table, (r − 1) × (c − 1). Degrees of freedom set the shape of the chi-square distribution used to get the p-value.
What does a significant chi-square result mean?
That the observed counts differ from what the hypothesis predicts more than chance would explain, the distribution doesn't fit, or the two variables are associated. It doesn't measure how strong the association is; for that, look at effect-size measures like Cramér's V.
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