P-Value Calculator
This p-value calculator converts a test statistic into a p-value for the standard normal (z), Student’s t, chi-square, or F distribution. Enter the statistic, choose a one-tailed or two-tailed test, and include degrees of freedom when they are needed. The result shows the p-value and the tail probabilities used to compute it.
P-value calculator
Enter a test statistic and choose the distribution and tail. Chi-square and F tests are usually right-tailed.
Working
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How to calculate a p-value
The method depends on the sampling distribution of your test statistic.
Z (standard normal): left p = Φ(z), right p = 1 − Φ(z), two-sided p = 2 × min(Φ(z), 1 − Φ(z)).
Student’s t with ν degrees of freedom: the same tail rules, using the t cumulative distribution instead of Φ.
Chi-square with k degrees of freedom: the usual test is right-tailed, so p = P(χ²k ≥ χ²).
F with df₁ and df₂: the usual test is right-tailed, so p = P(Fdf₁,df₂ ≥ F).
The calculator evaluates these probabilities with the normal, t, chi-square, and F distribution functions (the t, chi-square, and F probabilities use the regularized incomplete beta or gamma function).
Worked example
Suppose a z test gives z = 1.96 and you want a two-sided p-value.
The left-tail probability is Φ(1.96) ≈ 0.975002, and the right-tail probability is 1 − Φ(1.96) ≈ 0.024998. The two-sided p-value is 2 × 0.024998 ≈ 0.049996, or about 0.05. That is the familiar critical-value pairing: |z| = 1.96 is just at the 5% two-sided cutoff.
For a t test with t = 2.00 and 10 degrees of freedom, the two-sided p-value is about 0.0734, which is larger than the z p-value for the same statistic, because the t distribution has heavier tails.
How to use this calculator
- Choose the distribution that matches your test: z, t, chi-square, or F.
- Enter the test statistic. For a t test you also need degrees of freedom; for F you need both numerator and denominator df.
- Choose two-sided, left-tailed, or right-tailed. If you are not sure, two-sided is the usual choice for z and t, and right-tailed is the usual choice for chi-square and F.
- Read the p-value and the working, which shows both tail probabilities.
If you still need to compute the t statistic from raw data, use the t-test calculator. If you already have a t statistic only, the p-value calculator for a Student t-test covers that special case. The shorter URL /p-value-calculator/ currently redirects to that t-test-only tool, so this universal calculator lives at /pvalue-calculator/.
Related calculators and guides
Frequently asked questions
A p-value is the probability, under the null hypothesis, of getting a test statistic at least as extreme as the one you observed. A small p-value means the data would be unusual if the null hypothesis were true.
Use a two-tailed p-value when the alternative hypothesis is that the parameter is simply different from the null value (larger or smaller). Use a one-tailed p-value only when the alternative is directional and that direction was chosen before you saw the data. Chi-square and F tests are typically right-tailed.
No. A p-value below 0.05 is a conventional cutoff for statistical significance, but it is not proof, and it does not measure the size of an effect or the probability that the null hypothesis is true.
A z p-value uses the standard normal distribution and is appropriate when the sampling distribution is normal with a known standard error, or in large samples. A t p-value uses Student’s t distribution and is the usual choice when you estimated the standard deviation from the sample. With many degrees of freedom, the t p-value approaches the z p-value.
No. Chi-square and F statistics are never negative. If you have a signed statistic, use the z or t distribution instead.