🎯 P-Value Calculator
Find the p-value from a z, t, chi-square or F statistic, or a correlation r — one- or two-tailed, with critical values and a shaded curve.
Shaded: the p-value area. Solid line: your statistic. Dashed red: critical values for α = 0.05.
| P(X ≤ 1.96) — left tail | 0.9750 |
|---|---|
| P(X ≥ 1.96) — right tail | 0.0250 |
| Two-tailed | 0.0500 |
| Critical values at α = 0.05 | −1.96 and 1.96 |
What P-Value Calculator Does
This p-value calculator turns a test statistic into a p-value. Choose the distribution your test uses — the standard normal (z), Student’s t, chi-square or F — enter the statistic and its degrees of freedom, and pick a two-tailed, left-tailed or right-tailed test. You can also enter a Pearson correlation r with its sample size, and it is converted to a t statistic for you.
Alongside the p-value you get the decision at your significance level, the critical values that mark the rejection region, both tail areas, and a chart of the distribution with the p-value area shaded. Very small p-values are computed from the tail directly, so a two-tailed z of 8 shows about 1.2 × 10⁻¹⁵ instead of rounding to zero.
How to Use P-Value Calculator
- Choose the distribution: Z, t, chi-square, F or correlation r
- Enter the test statistic and its degrees of freedom
- Pick two-tailed, left-tailed or right-tailed
- Set the significance level α
- Read the p-value, the decision and the critical values
Formula Used by P-Value Calculator
P-value by tail
Right: p = P(X ≥ x) · Left: p = P(X ≤ x) · Two-tailed: p = 2 × min(P(X ≤ x), P(X ≥ x))
Worked example
t = 2.5 with 15 degrees of freedom, two-tailed.
- P(T ≥ 2.5) with 15 df = 0.0123
- 2 × 0.0123 = 0.0245
Result: p ≈ 0.0245 — significant at α = 0.05 but not at α = 0.01.
Correlation coefficient to t
t = r√(n − 2) ÷ √(1 − r²), with n − 2 degrees of freedom
Worked example
r = 0.4 from n = 30 pairs.
- t = 0.4 × √28 ÷ √0.84 = 2.309
- Two-tailed p with 28 df = 0.0285
Result: The correlation is significant at the 5% level.
Common Critical Values
| Distribution | α = 0.10 | α = 0.05 | α = 0.01 |
|---|---|---|---|
| z, two-tailed | 1.645 | 1.960 | 2.576 |
| z, one-tailed | 1.282 | 1.645 | 2.326 |
| t, two-tailed, 10 df | 1.812 | 2.228 | 3.169 |
| t, two-tailed, 30 df | 1.697 | 2.042 | 2.750 |
| χ², 1 df | 2.706 | 3.841 | 6.635 |
| χ², 5 df | 9.236 | 11.070 | 15.086 |
Which Test Uses Which Distribution
| Test | Statistic and degrees of freedom |
|---|---|
| Test of a mean with known σ, or a large-sample proportion test | z |
| One-sample or paired t test | t with n − 1 df |
| Two-sample t test (pooled) | t with n₁ + n₂ − 2 df |
| Chi-square goodness of fit | χ² with categories − 1 df |
| Chi-square test of independence | χ² with (rows − 1) × (columns − 1) df |
| One-way ANOVA | F with k − 1 and N − k df |
| Pearson correlation | t with n − 2 df |
How to Read Your Result
Reading the result
A p-value of 0.03 means that if the null hypothesis were true, a result at least this extreme would turn up about 3% of the time. Below α you reject the null hypothesis; above it you fail to reject it — which is not the same as showing it is true. Report the exact p-value rather than only “significant”.
Significance is not size
With a large enough sample, even a trivial effect becomes significant; with a small one, an important effect may not. Pair the p-value with an effect size and a confidence interval so readers can see how big the effect is and how precisely it was measured.
Many tests, more false alarms
At α = 0.05, about one in twenty tests of a true null hypothesis comes out significant by chance. When you run many tests, adjust for it — the Bonferroni correction, for example, divides α by the number of tests.
Limitations & Accuracy Notes
- The calculator converts a statistic you already have into a p-value; it does not run the test on raw data.
- Results assume the test’s conditions hold — for example, roughly normal data for a t test and expected counts of at least about 5 in each cell for chi-square.
- Exact tests for small samples, such as Fisher’s exact test or the binomial test, use other distributions and are not covered.