Global Calc Box logoGlobal Calc Box

Statistics

Chi-Square Calculator

Assess how well observed counts agree with expected counts using the chi-square goodness-of-fit test.

chi-squaregoodness of fitcategorical
Chi-square Goodness of Fit

Enter observed counts and expected counts to test distribution fit.

Chi-square statistic
1.1111
Degrees of freedom
2
p-value
0.573753

Chi-square statistic

χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ

The calculator also reports the degrees of freedom (categories − 1) and the corresponding right-tail p-value.

How to use

  1. Enter observed counts and matching expected counts.
  2. Ensure expected counts are positive and align with observed categories.
  3. Review χ², degrees of freedom, and the p-value.

Example

Input: Observed = 50,45,40; Expected = 45,45,45

Output: χ² ≈ 2.778, df = 2, p ≈ 0.249

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for Chi-Square Calculator: chi square calculator, chi square p value calculator, chi square goodness of fit calculator, chi square test statistic calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.

Step-by-step guideSee instructions, classroom tips, and practice prompts.Worked examplesReview the walk-through example plus try-it-yourself prompts.Category hubBrowse every tool in this category from one page.Statistics CalculatorFinds mean, median, variance, and standard deviation for a dataset.Variance CalculatorCalculates data variability around the mean as variance and standard deviation.Standard Deviation CalculatorComputes σ, variance, range, and coefficient of variation from any dataset.Probability CalculatorComputes event probabilities with percent, fraction, and odds outputs.

Deep dive & study plan

Chi-Square Calculator: Computes the chi-square statistic and p-value for goodness of fit. It's built around chi-square, goodness of fit, categorical, so you can go from a raw question to a checked answer without switching tools.

The math behind it: The calculator also reports the degrees of freedom (categories − 1) and the corresponding right-tail p-value. The core relationship is χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ, shown above the calculator so you can see exactly how your inputs turn into the result.

To use it well: (1) Enter observed counts and matching expected counts. (2) Ensure expected counts are positive and align with observed categories. (3) Review χ², degrees of freedom, and the p-value. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.

Worked example: entering Observed = 50,45,40; Expected = 45,45,45 returns χ² ≈ 2.778, df = 2, p ≈ 0.249. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.

FAQ & notes

Can I test contingency tables?

This calculator handles goodness-of-fit tests. For contingency tables, flatten the observed counts and compute expected frequencies first.

What if expected counts are zero?

Chi-square requires all expected counts to be positive. Combine categories or use Fisher’s exact test if counts are too small.

What formula does the Chi-Square Calculator use?

The calculator also reports the degrees of freedom (categories − 1) and the corresponding right-tail p-value.

How do I use the Chi-Square Calculator?

Enter observed counts and matching expected counts. Ensure expected counts are positive and align with observed categories. Review χ², degrees of freedom, and the p-value.