Chi Square Calculator Online
Last updated: July 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
What the Chi Square Calculator Online does
Under the hood, this calculator applies χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1, so the chi square calculator result you see is genuine math, not a lookup table.
For context, the sections beneath the calculator include typical values, a worked example you can recompute by hand, and an FAQ covering the practical details of chi square calculator.
Quick reference
| Input | Meaning |
|---|---|
| Observed | the counts you actually measured |
| Expected | the counts predicted under the null hypothesis |
| χ² | sum of (O − E)² ÷ E across categories |
| df | number of categories minus 1 |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
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Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
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Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
| p-value | Decision at α = 0.05 |
|---|---|
| p < 0.05 | Significant — observed differs from expected. |
| p ≥ 0.05 | Not significant — fits the expected distribution. |
| Larger χ² | Bigger gap between observed and expected counts. |
Formula & methodology
Formula: χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1
The chi-square goodness-of-fit test measures how far observed counts stray from expected counts. The p-value comes from the chi-square distribution with df = categories − 1.
- Enter the observed counts as a comma-separated list.
- Enter the expected counts in the same order.
- The calculator sums (O − E)² ÷ E to get χ².
- It finds df = categories − 1 and the p-value, with a verdict at α = 0.05.
Worked example: Observed 30, 20 vs expected 25, 25 gives χ² = 2.0, df = 1, p = 0.1573 — not significant.
Frequently asked questions
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