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P-Value Calculator

Choose the distribution, enter the test statistic and the degrees of freedom, and pick the tail. You get the p-value and whether it is below 0.10, 0.05 and 0.01.

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How we calculate it

The p-value is the probability, if the null hypothesis is true, of a test statistic at least as extreme as yours. For the right tail it is the area under the density curve to the right of the statistic, for the left tail the area to the left, and for the two-tailed z and t tests twice the area beyond the size of the statistic. For the chi-square and F distributions, which are not symmetric, the two-tailed value is twice the smaller tail, and the right tail is the usual choice.

The areas come from the incomplete gamma and beta functions, computed to about 15 digits, and the tails are worked out directly, so very small p-values keep their digits. For example, z = 1.96 gives a two-tailed p of 0.049996, so it is just below 0.05. A t of 2.228 with 10 degrees of freedom and a chi-square of 3.841 with 1 degree of freedom both give a p of about 0.05.

Assumptions and limits

  • A p-value does not give the probability that the null hypothesis is true, and it does not measure the size of an effect. It also depends on your choice of test and on the assumptions behind it.
  • The decision table uses p < α, the usual rule, and H0 stands for the null hypothesis. The significance level should be chosen before you look at the data.
  • The statistic can go up to 37 in size for z and 1,000,000 for the others, and the degrees of freedom up to 100,000 (they need not be whole numbers).

Frequently asked questions

What is a p-value?

It is the probability of getting a result at least as extreme as the one you saw if there were really no effect. A small p-value means the result would be unusual under the null hypothesis.

Should I use a one-tailed or a two-tailed test?

Use a two-tailed test when a difference in either direction matters, and a one-tailed test only if you decided in advance that you care about one direction. The two-tailed p-value of a symmetric test is double the one-tailed value.

What p-value counts as significant?

A common rule is p < 0.05, but there is nothing special about it. Some fields use 0.01 or stricter levels, and the table shows the result at 0.10, 0.05 and 0.01.

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Worked example (a fixed example using the starting numbers, it does not change as you type)

Inputs: Distribution = Standard normal (z-test); Test statistic = 1.96; Tail = Two-tailed.

  • p-value 0.049996
  • p-value (more digits) 0.0499957902964408
  • Distribution Standard normal (z)

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Last reviewed: . Formulas and assumptions are described on our methodology page. For information only; not professional advice.