P-Value Calculator
Translating a Test Statistic Into a Probability
A p-value answers one narrow question: if the null hypothesis were actually true, how likely would it be to observe a test statistic at least as extreme as the one calculated from the sample? It is not the probability the null hypothesis is true, and it is not the probability the results are due to chance — a common misreading. It is strictly a tail-area probability under the assumed null distribution, and this calculator derives it from four different distributions depending on which test produced the statistic.
The Formulas
Each distribution mode uses its own tail logic:
T distribution: same tail logic applied to the Student's t CDF with df degrees of freedom
Chi-Square: p = 1 − CDFχ²(x, df), right-tailed
F distribution: p = 1 − CDFF(x, df1, df2), right-tailed
Standard Significance Thresholds
| p-value range | Common interpretation |
|---|---|
| p ≥ 0.10 | Not significant |
| 0.05 ≤ p < 0.10 | Marginal / weak evidence |
| 0.01 ≤ p < 0.05 | Significant |
| p < 0.01 | Highly significant |
These thresholds are conventions, not universal rules — the appropriate alpha level depends on the field and the cost of a false positive.
Where This Calculation Matters
- Hypothesis testing — after computing any test statistic (z, t, χ², or F), the p-value is the final step that converts it into a decision against a chosen significance level.
- Reproducing textbook or software output — useful for checking a p-value reported by statistical software or in a paper when only the test statistic and degrees of freedom are given.
- Choosing tail direction — a directional (one-tailed) hypothesis, such as "the new process reduces defects," uses a different tail than a non-directional (two-tailed) one, and this calculator supports both.
How to Use This Calculator
- Choose the distribution type: From Z-Score, From T-Score, From Chi-Square Statistic, or From F-Statistic.
- Enter the test statistic value.
- For t, chi-square, and F distributions, enter the relevant degrees of freedom (df, or df1/df2 for F).
- For z and t distributions, choose Two-Tailed, Left-Tailed, or Right-Tailed.
- Select Calculate to get the resulting p-value.
Related Calculations
To find the threshold statistic for a given significance level instead of a p-value, use the Critical Value Calculator. For comparing two independent means, see the T-Test Calculator.