Chi Square Calculator

Solve χ² = Σ (O − E)² / E step by step — free chi square calculator with worked examples, real-world defaults and instant answers.

χ² = Σ (O − E)² / E

Observed counts O6 valuesExpected counts E (same order)6 values

χ² statistic22.4

Degrees of freedom5

p-value0.0004394

Verdict at α = 0.05Reject H₀ — distribution differs

1
One term per category — squared miss relative to expectation:
(18−20)²/20 = 0.2 (22−20)²/20 = 0.2 (16−20)²/20 = 0.8 (14−20)²/20 = 1.8 (12−20)²/20 = 3.2 (38−20)²/20 = 16.2
2
Sum the terms:
χ² = 22.4
3
Compare to χ² with k − 1 = 5 degrees of freedom:
p = 0.0004394

The default tests a die rolled 120 times — the pile of sixes (38 observed vs 20 expected) drives almost the whole χ². Rule of thumb: every expected count should be at least 5, and remember to use COUNTS, never percentages.

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Chi-square goodness of fit — observed vs expected counts, term by term.

About Chi Square Calculator

The Chi Square Calculator solves χ² = Σ (O − E)² / E for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. The default tests a die rolled 120 times — the pile of sixes (38 observed vs 20 expected) drives almost the whole χ².

How to use Chi Square Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into χ² = Σ (O − E)² / E and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Chi Square Calculator?

✓Solves χ² = Σ (O − E)² / E instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Chi Square Calculator use?+

It uses χ² = Σ (O − E)² / E. The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Chi Square Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

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