P-Value Calculator
p-value
0.04722396
P(|T₁₈| ≥ 2.13) = 0.04722396
Enter your test statistic
You need the statistic and degrees of freedom from your original test. This tool does not choose a test or analyse raw data.
Try a complete example
Tail area under the null model
Explore the statistic on the curve
Keyboard arrow keys work too. This is an explanation tool; do not choose the alternative after seeing the data.
Both one-sided areas
- Left of your statistic
- 0.976388
- Right of your statistic
- 0.02361198
For continuous distributions, including or excluding the boundary gives the same probability.
A p-value is conditional on the null model. It is not the probability that your hypothesis is true, an effect size, or proof of an important effect. Check the assumptions of the original test and report the study context.
How to use and interpret this result
Start with the test statistic from your calculation or statistical software. Select its distribution, copy its degrees of freedom and choose the alternative specified by your analysis. No measurements leave this page.
Which tail belongs to my test?
For z and t, a left alternative counts values at or below the observed statistic; a right alternative counts values at or above it. Two-tailed counts both directions at least as far from zero: p = 2 × the smaller one-sided area. A negative statistic does not automatically mean a left-tailed test.
The usual chi-square goodness-of-fit / independence tests and ANOVA F tests use the right tail. A left-tail option is available for a test that explicitly needs it. Two-sided variance tests require their own convention and are not calculated here; do not select a one-sided result as a replacement.
Small probabilities and numerical limits
The calculator evaluates incomplete gamma and beta functions with logarithmic tail probabilities. It does not round a small nonzero tail to zero. Results smaller than 1e-300 are shown as a bound; probabilities very close to one retain the small complement. Displayed answers use about seven significant digits, not exact decimals.
Supported statistics have magnitude at most 1,000,000; a nonzero magnitude must be at least 1e-100. Chi-square and F statistics must be nonnegative. Degrees of freedom may be fractional, from 0.1 to 100,000. These limits are computational support limits, not test validity criteria. The curve is clipped to a finite display range; shaded pixels are not used to calculate p.
What should I report?
Report the test, statistic, degrees of freedom, alternative and p-value together with the effect estimate and its uncertainty. A cutoff such as 0.05 is not a universal rule for a scientific, business or medical decision. Multiple testing and selecting analyses after seeing results need separate treatment.
For estimation from data, use the confidence interval calculator. For observed spread, use the standard deviation calculator; it serves a different task from a null-model tail.
Sources
NIST/SEMATECH reference distributions: normal, Student t, chi-square and F. Interpretation follows the American Statistical Association’s p-value statement.
Convert a z, t, chi-square or F statistic to a p-value. Inspect the selected tail and copy a reproducible result.
