Chi-Square Critical Value Calculator
Calculate critical Chi-Square values using degrees of freedom, significance level, and test type. Visualize the selected rejection region on an interactive Chi-Square distribution curve.
✓ Critical χ² values
✓ Interactive distribution
✓ One and two-tailed tests
✓ Step-by-step result
Visual probability
df = 5
Chi-Square Distribution
Selected region
P(χ² ≥ 11.0705)
Probability
0.0500
The Chi-Square distribution begins at zero and is right-skewed. Its shape changes with degrees of freedom.
Calculator
Find Critical χ² Values
Enter a positive whole number.
Calculated answer
Results
What this result means
For 5 degrees of freedom and α = 0.05, the upper critical Chi-Square value is approximately 11.0705. A test statistic above this value falls in the right-tail rejection region.
View Step-by-Step Solution
Practice numericals
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Degrees of Freedom
df = k − 1
For a basic goodness-of-fit test with k categories and no estimated parameters, degrees of freedom equal the number of categories minus one.
Degrees of Freedom
df = (r − 1)(c − 1)
For a contingency table, r is the number of rows and c is the number of columns.
Chi-Square Distribution
- Values begin at zero.
- The distribution is generally right-skewed.
- The shape changes with degrees of freedom.
- The mean equals the degrees of freedom.
Published: August 27, 2026
Last Updated: August 27, 2026
