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Mathematics · Statistics

P-Value Calculator — From z, t or Chi-square

Turn a test statistic into a p-value: a z-score, a t-statistic with its degrees of freedom, or a chi-square statistic with its degrees of freedom. Choose two-tailed, left- or right-tailed, compare with your significance level α, and see the critical value for that α.

Your inputs

Quick start — try a typical case

Your result Live

P-value

0.0357288 (3.5729%)

Significant at α = 0.05 — reject H₀ (the no-effect hypothesis)

Critical Value
±1.96 for α = 0.05
Test
z = 2.1, two-tailed

How this is calculated

z: p = 2(1 − Φ(|z|)) two-tailed · t: p = I_{ν/(ν+t²)}(ν/2, ½) two-tailed · χ²: p = Q(k/2, χ²/2)

Φ
Standard normal CDF
I, Q
Regularised incomplete beta and gamma functions

The p-value is the probability of a result at least as extreme as yours if the null hypothesis were true. A small p-value (below α, often 0.05) means the result would be surprising by chance alone, so it's called statistically significant. It isn't the probability that the hypothesis is true, and it says nothing about how large or important the effect is.

Assumptions & sources

  • The statistic follows the stated distribution under the null hypothesis.
  1. 1NIST/SEMATECH e-Handbook of Statistical Methods — US National Institute of Standards and Technology
  2. 2The ASA statement on p-values: context, process, and purpose — American Statistical Association, 2016

Calculator ID MATH-PVALUE-001 · version 1.0.0

Common questions

What's the p-value for z = 1.96?

0.05 two-tailed (0.025 in each tail).

Is p = 0.03 significant?

At α = 0.05 yes; at α = 0.01 no. Decide α before looking at the data.

One-tailed or two-tailed?

Two-tailed unless you decided in advance to test only one direction — a one-tailed test halves the p-value, so it mustn't be chosen after seeing the result.