About this p-value calculator
A p-value is the probability of getting a test statistic at least as extreme as the one you observed, assuming the null hypothesis is true. This calculator converts a z, t, chi-square or F test statistic into an exact p-value. You choose the distribution, enter the statistic and the degrees of freedom where needed, pick a one-tailed or two-tailed test, and read the p-value with a plain-language decision at your chosen significance level. It also gives the critical value for that level so you can use either the p-value method or the critical-value method.
The p-values come from the cumulative distribution functions of each distribution, calculated in your browser with the regularized incomplete gamma and beta functions. Nothing you enter is sent to a server.
Which statistic should you pick?
| Statistic | Typical use | Needs df? | Usual tail |
|---|---|---|---|
| z | Large-sample means, known population SD, proportion tests | No | Two-tailed or one-tailed |
| t | Small-sample means, paired and two-sample t-tests, regression coefficients | Yes (n − 1 for one sample) | Two-tailed or one-tailed |
| Chi-square (χ²) | Goodness of fit, tests of independence, variance tests | Yes | Right-tailed |
| F | ANOVA, comparing two variances, overall regression significance | Yes (two values) | Right-tailed |
How to use it
- Choose the distribution that matches your test and type the statistic from your software or hand calculation.
- Enter the degrees of freedom. For a one-sample t-test use n − 1. For chi-square goodness of fit use categories − 1. For a test of independence use (rows − 1) × (columns − 1). For an F-test enter both numerator and denominator df.
- Pick the tail. Use two-tailed when you are testing for any difference, right-tailed when you are testing for an increase, and left-tailed when you are testing for a decrease. Chi-square and F tests are almost always right-tailed.
- Read the result. If the p-value is less than or equal to your α, you reject the null hypothesis.
Worked examples
- t = 2.0, df = 10, two-tailed: p ≈ 0.0734. This is above 0.05, so you do not reject the null hypothesis at the 5% level.
- z = 1.96, two-tailed: p ≈ 0.0500. This is the familiar 95% cutoff.
- χ² = 3.841, df = 1, right-tailed: p ≈ 0.0500.
- F = 4.965, df₁ = 1, df₂ = 10, right-tailed: p ≈ 0.0500.
What a p-value does and does not tell you
A small p-value means the data would be surprising if the null hypothesis were true. It does not give the probability that the null hypothesis is true, it does not measure the size of an effect, and it does not prove your alternative explanation. A tiny p-value with a huge sample can reflect a trivial difference, and a large p-value with a small sample can hide a real one. Report the effect size and a confidence interval alongside the p-value, and decide your α before you look at the data.
Common mistakes
- Doubling twice or not at all. A two-tailed p-value is twice the smaller tail. Do not double a value that is already two-tailed.
- Wrong degrees of freedom. Using n instead of n − 1 changes the t result noticeably for small samples.
- Using a two-tailed p for a directional hypothesis or the reverse, after seeing which way the data points.
- Treating 0.05 as a cliff. p = 0.049 and p = 0.051 carry nearly the same evidence.
Related tools: get a statistic with the Z-Score Calculator, estimate a range with the Confidence Interval Calculator, summarize your data with the Standard Deviation Calculator, or fit a line with the Linear Regression Calculator.
Frequently asked questions
Choose the distribution (z, t, chi-square or F), enter the test statistic and any degrees of freedom, and pick the tail. The calculator returns the probability of a result at least that extreme under the null hypothesis. For a two-tailed test it doubles the smaller tail probability.
There is no universally good value. The most common rule is to call a result statistically significant when p is at or below 0.05, with stricter cutoffs such as 0.01 or 0.001 used in fields that need stronger evidence. The significance level should be set before you analyze the data.
A one-tailed p-value looks at one direction only, such as whether the mean is greater than a value. A two-tailed p-value counts extreme results in both directions, so it tests for any difference. For symmetric distributions like z and t, the two-tailed p-value is twice the one-tailed value.
For a one-sample or paired t-test, df is the number of observations minus 1. For a two-sample pooled t-test it is n1 + n2 minus 2. For chi-square goodness of fit it is the number of categories minus 1. For a chi-square test of independence it is (rows minus 1) times (columns minus 1). For F-tests you enter a numerator and a denominator df.
In theory no, but very extreme statistics give values too small to display, so the calculator shows them in scientific notation or as less than a tiny threshold. Report such a result as p < 0.0001 rather than p = 0.
It means the data are not unusual enough to reject the null hypothesis at the 5% level. That is not proof that the null hypothesis is true. The study may simply lack the sample size to detect a real effect.