A p-value tells you how surprising your z-score would be if nothing real were going on — the null hypothesis.
About this calculator
A p-value tells you how surprising your z-score would be if nothing real were going on — the null hypothesis. A small p-value (often below 0.05) means the result is unlikely under the null, so you may reject it. A large p-value means the data could easily happen by chance.
Enter your z-score and pick one-tailed or two-tailed. Two-tailed is standard for 'different from zero' questions. One-tailed fits directional claims like 'greater than' when you decided the direction before collecting data.
This calculator uses the standard normal CDF (same approximation as the [[z-score]] calculator). At z = 1.96 two-tailed, p ≈ 0.05. At z = 2.576, p ≈ 0.01.
Pair with the [[z-score]] calculator to convert raw data to z first, the [[confidence-interval]] calculator for interval estimates, and the [[sample-size]] calculator when planning a study.
Common uses
- Convert a z-test statistic to a p-value for a lab report
- Check whether |z| > 1.96 is significant at α = 0.05 two-tailed
- Compare one-tailed vs two-tailed significance for the same z
- Verify hypothesis-testing homework without a z-table
Frequently asked questions
What p-value corresponds to z = 1.96 two-tailed?
About 0.05. That is why ±1.96 is the critical value for a 95% confidence level on a normal curve — 5% of the area lies outside those bounds split across both tails.
When should I use a one-tailed test?
Use one-tailed only when you specified a direction before seeing data — for example,
How is p-value calculated from z-score?
For two-tailed: p = 2 × P(Z > |z|) using the standard normal CDF. For one-tailed with z ≥ 0: p = P(Z > z). With z < 0: p = P(Z < z).
Is p < 0.05 always meaningful?
No. Statistical significance is not the same as practical importance. A huge sample can make tiny effects significant. Always report effect size and context alongside p-values.