P-Value Calculator (z, t, Chi-Square and F)
Choose the test statistic’s distribution and enter its value and degrees of freedom.
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P-Value Calculator (z, t, Chi-Square and F) by TheCalcTools
How the P-Value Calculator (z, t, Chi-Square and F) works
The p-value is the probability, assuming the null hypothesis, of a statistic at least as extreme as the one observed. For z and t tests it can be two-sided or one-sided; chi-square and F tests use the right tail.
The t and F distributions are computed with the regularized incomplete beta function and the chi-square with the incomplete gamma function, to about 12 significant digits.
The formula
Worked example
Using the default values shown in the calculator:
| Distribution | Normal (z) |
|---|---|
| Test statistic | 1.96 |
| Degrees of freedom (df, or numerator df for F) | 12 |
| Denominator degrees of freedom (F only) | 20 |
| Tails (z and t) | Two-sided |
| Significance level α | 0.05 |
- z = 1.96 two-sided: p = 0.049996.
Result:
| p-value | 0.049996 |
|---|---|
| Conclusion | Significant at α = 0.05 |
| Cumulative probability below the statistic | 0.975002 |
Frequently asked questions
Is p = 0.05 a magic threshold?
No. It is a convention. Report the p-value and effect size, and consider the study design.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.