P-value Calculator
- Select distribution Z (Normal) and tail two-tailed.
- Evaluate the cumulative probability at score —, giving —.
- Apply the selected tail rule: p = 2 × min(F, 1 − F).
- Compare p with α = 0.05 to determine statistical significance.
- Normal CDF: Φ(z) = 0.5 × [1 + erf(z / √2)]
- t CDF via the regularized incomplete beta function
- χ² CDF via the regularized lower incomplete gamma function
- F CDF via the regularized incomplete beta function
Use this P-Value Calculator to convert an already-calculated Z, t, chi-square, or F test statistic into a left-tailed, right-tailed, or supported two-tailed p-value.
Calculation Method
The calculator first evaluates the cumulative distribution function for the selected distribution.
For a cumulative probability F(x):
Left-tailed p-value = F(x)
Right-tailed p-value = 1 − F(x)
For symmetric Z and t distributions, a two-tailed p-value can be calculated as:
p = 2 × min[F(x), 1 − F(x)]
Example
For a z-score of 2.00 with a two-tailed alternative:
The upper-tail probability is approximately:
0.02275
Therefore:
p ≈ 2 × 0.02275 = 0.0455
At α = 0.05, this result would be statistically significant because 0.0455 < 0.05.
Important Note
A p-value is calculated assuming the null hypothesis and statistical model are correct. It is not the probability that the null hypothesis is true and does not measure effect size or practical importance.
Select the distribution, degrees of freedom, and tail direction that match the original statistical test. Two-tailed interpretation for chi-square and F distributions is test-specific and may not follow the same convention as symmetric Z or t tests.