P-value Calculator
p = 0
What This Calculator Actually Does
This tool converts an already-computed test statistic (a z-score, t-score, chi-square value, or F-score) into a p-value. It does not compute the test statistic from raw sample data — for that you first need the appropriate hypothesis test (e.g. a t-test formula) to reduce your data to a single statistic, then bring that number here to find its p-value. The p-value itself is the probability, under the null hypothesis, of observing a test statistic at least as extreme as the one you entered.
Choosing One-Tailed vs. Two-Tailed
A two-tailed test asks whether the statistic is unusually far from zero (or from the expected value) in either direction, and is the standard, more conservative choice when you have no prior expectation about the direction of an effect. A one-tailed test asks whether it's unusually far in one specific direction only, and should only be used when that direction was decided before looking at the data. For the z and t distributions, the two-tailed p-value is simply twice the one-tailed p-value on the relevant side, since both distributions are symmetric about zero. Chi-square and F statistics are non-negative and right-skewed, so they are conventionally tested one-tailed (right tail) for goodness-of-fit, independence, and variance-ratio tests.
Reading Your Result
A small p-value (typically below your chosen significance level α, commonly 0.05) means the observed statistic would be rare if the null hypothesis were true, so you reject the null hypothesis. A p-value above α means the data are not surprising enough to reject it — this is not proof the null hypothesis is true, only that you lack sufficient evidence against it. If you need to compute z-scores or work through the underlying probability distributions first, see the z-score calculator and statistics calculator.
Frequently Asked Questions
Does this calculator compute the test statistic from my raw data?
No. You must already have a z-score, t-score, chi-square value, or F-score from a hypothesis test (or from the z-score calculator). This tool only converts that statistic into a p-value; it does not perform the underlying test on raw sample data.
Should I use a one-tailed or two-tailed test?
Use two-tailed unless you had a specific directional prediction decided before collecting your data. Two-tailed tests check for a difference in either direction and are the more common, more conservative default. Chi-square and F tests are non-negative and are conventionally evaluated one-tailed (right tail).