Chi-Square Calculator

Goodness of fit, with the expected-count rule checked.

Goodness of fit, with the expected-count rule checked. Enter observed and expected counts for the chi-square statistic, degrees of freedom and p value.

Written and maintained by Mohit PatelLast checked August 4, 2026How we build these

Observed counts

Comma separated, in the same order as the expected counts.

Expected counts

Significance level

Chi-square statistic

p = 0.1573 · 1 degrees of freedom

Chi-square2

p value0.157299

Degrees of freedom1

Significant?No

ConclusionDo not reject the null at α = 0.05 — the counts are consistent with the expected distribution

χ² = Σ (observed − expected)² / expected, summed across categories. It measures how far a set of counts strays from what a hypothesis predicts. Degrees of freedom for a goodness-of-fit test is the number of categories minus one, because once all but one category is known the last is determined by the total.

How the Chi-Square Calculator works

Enter observed and expected counts for the chi-square statistic, degrees of freedom and p value. The page warns when any expected count falls below 5, which is the point at which the approximation stops being reliable.

Also known as: chi square test calculator · goodness of fit calculator · chi square p value calculator · observed vs expected calculator

Where to go next

The Chi-Square question rarely arrives on its own. These are the ones that usually come with it:

T-Test Calculator — One-sample t-test, with what a p value does not mean.
Margin of Error Calculator — Why polls stop at a thousand people.
Percentage Calculator — Every common percentage question in one place.
Age Calculator — Exact age in years, months, days, and total units.

Sources

NIST Digital Library of Mathematical Functions

Frequently asked questions

What is the chi-square statistic?

Σ (observed − expected)² / expected, summed across categories. It measures how far a set of counts strays from what a hypothesis predicts, weighting each category by how much was expected there.

Why must expected counts be at least 5?

Because chi-square approximates a discrete distribution with a continuous one, and that approximation degrades badly with small counts. Below 5 the p value is unreliable and Fisher's exact test is the better choice.

How many degrees of freedom?

Categories minus one for a goodness-of-fit test. Once all but one category is known the last is fixed by the total, so only k−1 are free.

Can chi-square use percentages?

No. It needs actual counts. Feeding it percentages makes the statistic depend on your choice of scale rather than on the evidence, and 60/40 from 10 observations is treated identically to 60/40 from 10,000.

Put this calculator on your own site

Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.

The one-line version

<iframe src="https://www.thecalclibrary.com/embed/chi-square-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Chi-Square Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/chi-square-calculator" style="color:#64748b">Chi-Square Calculator</a> from The Calc Library</p>

The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.