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Chi-Square Calculator | Compute χ² From Observed And Expected

Compute the chi-square statistic from observed and expected counts, with the degrees of freedom and p-value included. Run goodness-of-fit and independence tests with every term of the formula displayed.

Last updated: July 2026 · Free · No sign-up required

Results

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

InputMeaning
Observedthe counts you actually measured
Expectedthe counts predicted under the null hypothesis
χ²sum of (O − E)² ÷ E across categories
dfnumber of categories minus 1

info Chi Square Calculator Online

Free math calculator — enter your numbers and get an instant, accurate result.

info Private by design

Everything runs locally in your browser. No uploads, no accounts, no tracking.

info Works everywhere

Fully responsive and mobile-friendly — calculate on any device, any time.

info Educational

Includes the formula and step-by-step explanation so you understand the math, not just the answer.

Interpretation guide

p-valueDecision at α = 0.05
p < 0.05Significant — observed differs from expected.
p ≥ 0.05Not significant — fits the expected distribution.
Larger χ²Bigger gap between observed and expected counts.

lightbulb Worked example

Let's say you are using the Chi Square Calculator Online. Calculates chi square using χ² = Σ (Observed − Expected)² ÷ Expected, live in your browser. Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1 and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1

The Chi Square Calculator Online is built on a well-established calculation method. It uses the formula χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1 to turn your inputs into a reliable result. Calculates chi square using χ² = Σ (Observed − Expected)² ÷ Expected, live in your browser. The steps are shown on the page so you can follow the reasoning from input to output.

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.

  1. Enter the observed counts as a comma-separated list.
  2. Enter the expected counts in the same order.
  3. The calculator sums (O − E)² ÷ E to get χ².
  4. 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.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How do you calculate a chi-square statistic?
Enter the required values into the input fields and press the calculate button. The tool applies the formula χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1 and returns the result with a short explanation of each step, so you can check the working yourself.
What does the p-value tell me?
The Chi Square Calculator Online is a free online tool that calculates chi square using χ² = σ (observed − expected)² ÷ expected, live in your browser. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
What are the degrees of freedom?
Yes — the Chi Square Calculator Online. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
What is a chi-square goodness-of-fit test used for?
It tests whether observed frequencies match an expected distribution — for example, whether a die is fair (each face expected 1/6 of rolls), whether customer preferences match a claimed split, or whether survey responses fit a hypothesized pattern. The statistic χ² = Σ (observed − expected)² ÷ expected measures the total deviation, compared against the chi-square distribution with categories − 1 degrees of freedom.
Is it free and private to use?
Yes — the calculator is completely free with no sign-up or limits, and all computations run in your browser so your observed and expected counts never leave the page. CalcaTools covers its costs with display advertising. The tool returns the chi-square statistic, the degrees of freedom, and the p-value for your test.
What is the chi-square distribution and when do I use it directly?
It's the distribution of a sum of k squared standard normals, where k is the degrees of freedom — always right-skewed, always non-negative, with mean k. You consult it directly for critical values: at df = 5, the 5% cutoff is 11.07, so a test statistic above that rejects at α = 0.05. Goodness-of-fit and independence tests both reduce to this lookup.
What does the Chi Square Calculator Online do?
Calculates chi square using χ² = Σ (Observed − Expected)² ÷ Expected, live in your browser. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Chi Square Calculator Online use?
It computes χ² = Σ (Observed − Expected)² ÷ Expected across all categories, with degrees of freedom df = categories − 1. Enter the observed and expected counts and the tool returns the chi-square statistic, which you compare against the critical value for your df. A larger statistic means more evidence that the observed distribution differs from the expected one.
Is the Chi Square Calculator Online free and private?
Yes — it is free with no sign-up, paywall, or usage limits, and the calculation runs entirely in your browser so no data is uploaded. CalcaTools funds itself with display ads. The tool computes the chi-square statistic and p-value for goodness-of-fit and independence tests, with the working shown step by step.
How accurate is the Chi Square Calculator Online?
The Chi Square Calculator Online applies the standard formula: χ² = Σ (Observed − Expected)² ÷ Expected; df = categories − 1. It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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