Chi Square Calculator
The Chi-Square Calculator compares observed counts to expected counts across categories using the goodness-of-fit formula, returning the chi-square statistic and its degrees of freedom.
What this calculator does
The Chi Square Calculator estimates your result instantly from the values you enter, using standard statistics formulas. The Chi-Square Calculator compares observed counts to expected counts across categories using the goodness-of-fit formula, returning the chi-square statistic and its degrees of freedom. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.
Result
About Chi Square Calculator
Enter a list of observed counts and a matching list of expected counts, and this tool computes the chi-square goodness-of-fit statistic, which measures how far your observations stray from what was expected. It also reports the degrees of freedom.
The two lists must be the same length and every expected value must be greater than zero.
Formula & Mathematical Calculation
Chi-Square (χ²) = f(Observed values (comma-separated), Expected values (comma-separated))
Calculated according to standard stats formulas implemented in the calculator core.
Calculation Example
For observed counts 20, 30, 25 against expected counts 25, 25, 25, each term is the squared difference divided by the expected value: (20−25)²÷25 + (30−25)²÷25 + (25−25)²÷25 = 25÷25 + 25÷25 + 0.
That sums to χ² = 1 + 1 + 0 = 2, with degrees of freedom equal to 3 − 1 = 2.
Key Benefits
- Computes the chi-square goodness-of-fit statistic from observed and expected counts
- Reports the degrees of freedom for looking up a critical value
- Handles any equal-length pair of category lists
- Checks that every expected value is positive before calculating
How to Use this Calculator
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Enter observed values
Type your observed counts into the Observed values field, separated by commas. -
Enter expected values
Type the matching expected counts into the Expected values field, using the same number of entries. -
Calculate
Press Calculate and read the Chi-Square and Degrees of Freedom boxes.
Assumptions & Limitations
What the calculation assumes
- Every value you enter is treated as an exact, known amount.
- Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
- Results use standard published formulas and account only for the values entered above.
- Rounding is applied for display; the underlying calculation uses your full precision.
- Results are returned in the same units you enter, unless the tool states the output unit.
What it does not cover
- Chi Square Calculator produces a calculated result for reference and learning, not a certified or official measurement.
- Real-world outcomes differ when tolerances, rounding rules or local standards apply.
- Definitions and standards vary by region and change over time; verify the convention that applies to your case.
- Figures are only as accurate as the inputs you supply — check them before acting on the result.
- For work where the result carries real consequences, confirm it against an authoritative source.
Frequently Asked Questions
Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.