Critical Value Calculator (z, t, χ², F)

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Critical Value Calculator

This critical value calculator gives the cut-off that a test statistic must pass for you to reject the null hypothesis. Choose the distribution, enter α and the degrees of freedom, and select a left-, right- or two-tailed test. The result states the rejection rule in words.

For a two-tailed test, α is split equally between the tails, so at α = 0.05 the z critical values are ±1.960 and each tail holds 0.025. A right-tailed z-test at 0.05 uses 1.645 instead. For t the values are larger than z when degrees of freedom are small, which is why a t-interval from 5 observations is wider than a z-interval. Chi-square and F distributions are not symmetric, so the two-tailed option returns separate lower and upper values.

Critical values are also what you need to build a confidence interval: the 95% interval for a mean uses the two-tailed 0.05 t value. Printable versions are on the z-table, t-table, chi-square table and F-table pages, and the p-value calculator answers the reverse question.

Frequently asked questions

What is the critical value for a 95% confidence interval?

For z it is 1.960. For t it depends on the degrees of freedom: 2.262 for df = 9, 2.042 for df = 30 and close to 1.96 for very large df.

What is the z critical value for α = 0.05 one-tailed?

1.645 for a right-tailed test and −1.645 for a left-tailed test.

How do I use a critical value?

Compare your test statistic with it. If the statistic falls beyond the critical value (in the rejection region), reject the null hypothesis.

Why are two-tailed critical values larger?

Because α is split between two tails, each tail holds only α/2, so you have to go further from the centre to leave that smaller area.

Last reviewed: October 7, 2026. Calculations run in your browser and were validated against SciPy.