Chi-Square Test Calculator
Calculate the chi-square (χ²) statistic for goodness-of-fit or independence tests. Enter observed and expected frequencies to get χ² and p-value.
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How to use this calculator
Sum the squared difference between observed (O) and expected (E) frequencies divided by expected, across all categories.
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Enter observed frequencies (actual counts) for each category.
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Enter expected frequencies (what you would expect under the null hypothesis).
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The calculator returns χ² and the p-value for df = categories − 1.
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If p < α, the observed distribution significantly differs from expected.
Frequently asked questions
What is the chi-square test used for?
Chi-square tests determine whether observed categorical data matches an expected distribution (goodness-of-fit) or whether two categorical variables are independent of each other (independence test).
What are degrees of freedom in chi-square?
Degrees of freedom = number of categories − 1 for goodness-of-fit tests. For contingency tables: df = (rows − 1) × (columns − 1).
What sample size do I need?
Expected frequencies should be at least 5 in each cell. If any expected frequency is below 5, consider merging categories or using Fisher's exact test instead.
Chi-Square Test Calculator — χ² Statistic & P-Value
How to use the chi-square test
Use this chi-square test to he chi-square (χ²) statistic for goodness-of-fit or independence tests. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the chi-square test works
The chi-square test calculator uses standard formulas used in statistical analysis, data science, and research. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
When to use the chi-square test
Use the goodness-of-fit chi-square test to compare an observed frequency distribution against a theoretical one — for example, checking if dice rolls are fair. Use the chi-square test of independence to test whether two categorical variables (like gender and voting preference) are related.
Assumptions and limitations
Chi-square tests require: independent observations; categorical data; expected frequencies of at least 5 per cell. The test tells you whether a difference exists, not how large or important the difference is — combine it with effect size measures like Cramér's V.
Chi-square test: how it works
Statistical analysis underpins data science, research, quality control, and business intelligence. This tool applies established textbook formulas to your dataset and returns results instantly, eliminating manual calculation errors.
Who uses this tool?
Researchers, students, analysts, and business professionals use it to understand datasets quickly. Whether you are summarising survey responses or checking experiment results, this tool delivers the key figures instantly.
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