Free research tool
P-value calculator
Enter your test statistic — z-score or t-statistic — and get the exact p-value, one- or two-tailed, with a plain-language reading at α = 0.05.
P-value
0.0500
How it works
The p-value is the probability, under the null hypothesis, of a statistic at least as extreme as yours. Two-tailed doubles the smaller tail:
p = 2 · (1 − Φ(|z|)) · or with the t-CDF for t-statistics
The normal CDF uses the Abramowitz–Stegun erf approximation (error < 1.5×10⁻⁷); the Student-t CDF uses the regularized incomplete beta function. At large degrees of freedom the t result converges to the z result — try t = 1.96 with df = 10,000.
Frequently asked questions
How do I get a p-value from a z-score?
The p-value is the tail area of the standard normal distribution beyond your z. Two-tailed: p = 2·(1 − Φ(|z|)). For z = 1.96 that gives p = 0.05.
When do I use t instead of z?
Use the t-distribution when the population standard deviation is unknown and estimated from the sample — the usual case. It needs degrees of freedom (typically n − 1); at large df it converges to z.
Is p < 0.05 the only threshold that matters?
No — 0.05 is convention, not law. Report the exact p-value; fields differ (0.01, 0.005), and effect size matters as much as significance.