About the P-Value Calculator
This p-value calculator converts a test statistic into the probability of seeing a result at least that extreme if the null hypothesis were true. Choose the distribution your test uses — the standard normal (z), Student’s t, chi-square (χ²) or F — enter the statistic and its degrees of freedom, pick a left-, right- or two-tailed test, and it returns the p-value and a plain-English significance decision.
Use it after running a z-test or t-test on means or proportions, a chi-square test of independence or goodness of fit, or an ANOVA / regression F-test, when your software or textbook gives you the statistic but not the p-value. It is also a quick way to check a p-value table lookup.
The p-values are computed directly from each distribution’s cumulative distribution function (via the regularized incomplete gamma and beta functions) rather than read from a printed table, so you get the p-value to six or more decimal places instead of a range such as "0.01 < p < 0.025".
With the default inputs, the p-value is 0.049996. Change any value above to recalculate instantly.
How to use the p-value calculator
- 1Pick the distribution your test uses: z, t, chi-square or F.
- 2Enter the test statistic from your analysis.
- 3Enter the degrees of freedom (two values for an F-test).
- 4Choose two-tailed for "≠" hypotheses, or left/right for one-sided ones.
- 5Compare the p-value with α to decide whether the result is statistically significant.
Formula and method
The p-value is the area in the tail(s) of the test statistic’s distribution beyond the observed value. For a two-tailed test both extremes count, so the smaller tail is doubled. For the normal distribution the tail area comes from the error function; for Student’s t, chi-square and F it comes from their cumulative distribution functions.
The calculator evaluates those CDFs numerically to high precision: t and F use the regularized incomplete beta function, e.g. P(|T| > t) = I_{ν/(ν+t²)}(ν/2, 1/2), and chi-square and z use the regularized incomplete gamma function. If p ≤ α you reject the null hypothesis at that significance level.
- x
- Observed test statistic (z, t, χ² or F)
- ν, df
- Degrees of freedom (numerator and denominator for F)
- α
- Significance level, commonly 0.05
- H₀
- Null hypothesis being tested
Worked examples
Two-tailed z-test, z = 1.96
z = 1.96 leaves about 2.5% in the upper tail; doubling it for a two-tailed test gives p ≈ 0.0500, right on the conventional 0.05 cut-off.
t = 2.5 with 15 degrees of freedom
With 15 df the t distribution has heavier tails than the normal, so t = 2.5 gives a two-tailed p of about 0.0246 — significant at the 5% level but not at 1%.
Chi-square 7.5 with 3 df (right-tailed)
The area above χ² = 7.5 with 3 degrees of freedom is about 0.0576, just above 0.05, so the result is not significant at α = 0.05.
ANOVA F = 4.2 with 2 and 27 df
An F statistic of 4.2 with 2 numerator and 27 denominator degrees of freedom has a right-tail p ≈ 0.0258, so the group means differ significantly at the 5% level.
Frequently asked questions
What does a p-value mean?+
It is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value means the data would be surprising under the null hypothesis.
Is p = 0.05 significant?+
By the usual convention a result is significant when p ≤ α, so p = 0.05 is borderline significant at α = 0.05. The 0.05 threshold is a convention, not a law — report the exact p-value and effect size.
Should I use a one-tailed or two-tailed test?+
Use two-tailed when your alternative hypothesis is "different from" (≠). Use one-tailed only if you specified the direction (greater than or less than) before seeing the data. A one-tailed p is half the two-tailed p for z and t.
How do I find degrees of freedom?+
For a one-sample t-test df = n − 1; for a chi-square test of independence df = (rows − 1)(columns − 1); for one-way ANOVA the F df are (k − 1) and (N − k), where k is the number of groups and N the total sample size.
Does a small p-value mean the effect is large?+
No. A p-value measures evidence against the null, not the size or importance of an effect. With a large sample, tiny effects can be highly significant, so look at confidence intervals and effect sizes too.