Chi-Square Calculator – Test of Independence & P-Value in 3 Easy Steps

Use this free chi-square calculator to run a chi-square test of independence on a contingency table or a goodness of fit test on one variable. You get the chi-square statistic, degrees of freedom, p-value, critical value and the expected count for every cell.

Survey results, A/B test conversions, genetics ratios and quality control counts all end up as categories with counts. The chi-square test tells you whether the pattern you see is likely real or just random noise.

Doing it by hand means working out every expected value, summing the terms and then looking up a p-value table. This chi-square calculator does all of that instantly and flags any expected count below 5, so you know when the result needs care.

What Is a Chi-Square Test?

A chi-square (χ²) test is a statistical test for categorical data. It measures how far the counts you observed are from the counts expected under a null hypothesis. A small χ² means observed and expected are close. A large χ² means they are far apart, and the p-value tells you how unusual that gap would be if the null hypothesis were true.

The calculator covers the two most common versions:

• Test of independence: checks whether two categorical variables are related, for example gender and product preference. Data goes in a contingency table.
• Goodness of fit: checks whether one variable follows an expected distribution, for example whether a die is fair or whether sales are spread evenly across four regions.

Chi-Square Formula

• Chi-square statistic: χ² = Σ (O − E)² ÷ E, summed over every cell
• Expected count (independence): E = (row total × column total) ÷ grand total
• Expected count (goodness of fit): E = total observed × expected proportion
• Degrees of freedom: (rows − 1) × (columns − 1) for independence, or categories − 1 for goodness of fit
• Cramér’s V (effect size): √[χ² ÷ (N × (k − 1))], where k is the smaller of rows or columns

The p-value is the area to the right of your χ² value under the chi-square distribution with the matching degrees of freedom. The calculator works this out exactly, so you do not need a printed table.

Chi-Square Critical Values Table

If you want to check a result by hand, compare your χ² with the critical value for your degrees of freedom. Values above the critical value are significant.

How to Use the Chi-Square Calculator

The example below tests whether three product versions are preferred differently by two customer groups of 50 and 70 people.

Step 1: Choose the Test and Enter Your Counts

Keep Test of Independence selected, set the number of rows and columns, and type the observed count in each cell. Pick a significance level; 0.05 is the usual choice. Use raw counts, not percentages.

Step 2: Calculate and Read the Result

Press Calculate Chi-Square. Here χ² = 14.9143 with 2 degrees of freedom, so the p-value is 0.0006. That is far below 0.05 and above the 5.9915 critical value, so the two groups do not share the same preferences. Cramér’s V of 0.353 points to a moderate association. The expected counts table shows what each cell would hold if there were no relationship.

Step 3: Run a Goodness of Fit Test

Switch to Goodness of Fit to test one variable. Enter the observed counts, then choose whether the expected values are equal, raw counts or percentages. In this example 120 observations are tested against an expected split of 40%, 30%, 15% and 15%. The result is χ² = 1.4167 and p = 0.7016, so the data fit the expected pattern well.

When Can You Use a Chi-Square Test?

• Your data are counts (frequencies) in categories, not means or percentages.
• Each observation falls into exactly one cell and observations are independent of each other.
• Expected counts are 5 or more in at least 80% of cells, and none is below 1. The calculator warns you when expected counts are small.
• For a 2×2 table with very small counts, Fisher’s exact test is the safer option.

Chi-Square Test Example: A/B Test Conversions

Say version A of a page got 120 sign-ups from 1,000 visitors and version B got 150 from 1,000. Enter a 2×2 table with sign-ups and non-sign-ups (120, 880 and 150, 850). The calculator returns χ² ≈ 3.85 with 1 degree of freedom and p ≈ 0.0496. That is only just below 0.05, so B wins at the 5% level, but the margin is thin. Many teams would keep the test running a little longer before rolling out the change.

To measure the effect on revenue once you have a winner, try the CRO Calculator. For numeric data instead of counts, the ANOVA Solver or Pearson Correlation Calculator is the better fit.

Frequently Asked Questions