Chi-Square Test Calculator
Calculate the chi-square statistic, degrees of freedom, and p-value for goodness-of-fit and independence tests instantly with our free chi-square test calculator. Supports contingency tables up to 5×5 with a cell-by-cell contribution breakdown — all processed locally in your browser. No signup required.
Select the test type, enter your observed (and expected) values, and click Calculate. The chi-square statistic, degrees of freedom, p-value, and significance decision are computed instantly in your browser — no data is ever sent to any server.
Observed vs. Expected Values
| Category | Observed (O) | Expected (E) | |
|---|---|---|---|
Why Use Our Chi-Square Test Calculator?
Instant Chi-Square Test Calculations
Calculate the chi-square statistic, degrees of freedom, p-value, and critical value in milliseconds. Our chi-square test calculator supports both goodness-of-fit and test of independence — all processed instantly in your browser.
Secure Chi-Square Calculator Online
All chi-square calculations run 100% locally in your browser. Your data never leaves your device — use our chi-square test calculator online with complete privacy and zero data collection.
Chi-Square Calculator — No Installation
Use our chi-square test calculator directly in any browser with no downloads, plugins, or app installs required. Run chi-square tests from any device, anywhere, with no setup needed.
Cell-by-Cell Contribution Breakdown
Every chi-square calculation shows the (O−E)²/E contribution of each cell, making it easy to identify which categories or cells drive the chi-square statistic. Supports contingency tables up to 5×5.
Common Use Cases for Chi-Square Test Calculator
Statistics & Research Education
Students learning hypothesis testing use the chi-square test to analyse categorical data. Our chi-square test calculator shows the full calculation breakdown — chi-square statistic, degrees of freedom, p-value, and significance decision.
Scientific Research & Genetics
Biologists use the chi-square goodness-of-fit test to compare observed genetic ratios against Mendelian expected ratios. Our calculator handles any number of categories with exact p-values.
Market Research & Surveys
Analysts use the chi-square test of independence to determine whether two categorical variables — such as product preference and age group — are related. Our contingency table calculator supports up to 5×5 tables.
Medical & Clinical Research
Clinical researchers use chi-square tests to analyse treatment outcomes, disease prevalence across groups, and diagnostic test performance. Our calculator provides exact p-values for any contingency table.
A/B Testing & Conversion Analysis
Product teams use chi-square tests to determine whether conversion rate differences between variants are statistically significant. Enter observed conversions and non-conversions for each variant as a 2×2 contingency table.
Data Science & Machine Learning
Data scientists use chi-square tests for feature selection — identifying which categorical features are statistically associated with the target variable. Our calculator verifies chi-square computations instantly.
Understanding the Chi-Square Test
What is the Chi-Square Test?
The chi-square test (χ²) is a statistical hypothesis test used to analyse categorical data. It compares observed frequencies with expected frequencies to determine whether any difference is due to chance or reflects a real effect. There are two main types: the goodness-of-fit test (does one variable follow an expected distribution?) and the test of independence (are two categorical variables related?). Our chi-square test calculator computes the exact chi-square statistic, degrees of freedom, and p-value using the regularised incomplete gamma function.
How Our Chi-Square Test Calculator Works
- 1. Select test type and α: Choose goodness-of-fit or test of independence, and set your significance level (typically α = 0.05).
- 2. Enter your data: For goodness-of-fit, enter observed and expected counts per category. For independence, fill in the contingency table cells.
- 3. Get instant results: Click Calculate to see χ², df, p-value, critical value, significance decision, and a cell-by-cell contribution breakdown — all processed locally in your browser.
The Chi-Square Formula
Sum over all categories or cells. O = observed frequency, E = expected frequency. Larger χ² means greater deviation from the null hypothesis.
k = number of categories; r = rows; c = columns. df determines the shape of the chi-square distribution used to find the p-value.
Expected frequencies are calculated from the marginal totals under the assumption of independence. Each expected cell should ideally be ≥ 5 for the chi-square approximation to be valid.
Key Assumptions & Limitations
- Expected cell frequency ≥ 5: The chi-square approximation is most reliable when all expected frequencies are at least 5. For smaller samples, consider Fisher's exact test.
- Independent observations: Each observation must be independent — the chi-square test is not appropriate for paired or repeated-measures data.
- Categorical data only: The chi-square test applies to counts of categorical variables, not continuous measurements or proportions.
- p-value interpretation:A significant p-value (p < α) means the data are unlikely under the null hypothesis — it does not measure the size or practical importance of the effect.
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Frequently Asked Questions About Chi-Square Test Calculator
A chi-square test calculator computes the chi-square statistic (χ²), degrees of freedom, p-value, and critical value for categorical data. Our calculator supports both the goodness-of-fit test and the test of independence, with a cell-by-cell contribution breakdown — all processed instantly in your browser with no signup required.
The goodness-of-fit test checks whether one categorical variable follows an expected distribution (e.g. are dice rolls equally likely?). The test of independence checks whether two categorical variables are related (e.g. is product preference independent of age group?). Both use the same χ² formula but differ in how expected values are calculated and in the degrees of freedom.
If the p-value is less than your significance level α (typically 0.05), you reject the null hypothesis — the observed data differ significantly from expected (goodness-of-fit) or the two variables are not independent (independence test). If p ≥ α, you fail to reject the null hypothesis.
Degrees of freedom (df) determine the shape of the chi-square distribution used to find the p-value. For goodness-of-fit: df = k − 1 (k = number of categories). For independence: df = (rows − 1) × (columns − 1). A 2×2 contingency table has df = 1.
The chi-square approximation is most reliable when all expected cell frequencies are at least 5. If some expected frequencies are below 5, the chi-square test may be inaccurate. In such cases, consider combining categories or using Fisher's exact test for 2×2 tables.
For a test of independence, the expected frequency for cell (r, c) is: E = (Row Total × Column Total) / Grand Total. This represents the frequency you would expect if the two variables were completely independent of each other.
Yes, completely. All chi-square calculations run 100% locally in your browser using JavaScript. Your data is never sent to any server, stored, or logged. Use our chi-square test calculator online with full confidence in your privacy.
Yes. Our chi-square test calculator is 100% free with no signup, no account, no premium tier, and no usage limits. Run chi-square tests as many times as you need — completely free, forever.
The most common significance level is α = 0.05 (5%), meaning you accept a 5% chance of a false positive. For more stringent research, use α = 0.01 or α = 0.001. For exploratory analysis, α = 0.10 is sometimes used. Our calculator supports all four common levels.