A familiar situation
Convert a z statistic to a tail probability when interpreting a planned normal-theory test.
How to use this calculator
- Enter z statistic, alternative hypothesis.
- Select Calculate to see the answer and its breakdown.
- Keep a scenario, change an input and compare the results.
Use consistent units and check the assumptions below before applying the result.
How p-value is calculated
For standard normal Z, left tail is Φ(z), right tail is 1−Φ(z), and two-tail is 2[1−Φ(|z|)]. A numerical approximation evaluates Φ. The p-value is conditional on the null model and chosen tail direction; it is neither the probability that the null is true nor a measure of effect size. A z score of 1.96 gives a two-sided p-value of about 0.05.
Left tail Φ(z); right tail 1−Φ(z); two-sided 2[1−Φ(|z|)].A z score of 1.96 gives a two-sided p-value of about 0.05.
Assumptions & useful context
The result depends on the values you enter and the method described above. Displayed numbers may be rounded; calculations use the unrounded values. Check that this model matches your situation before relying on it.
Frequently asked questions
Does a small p-value prove the hypothesis is true?
No; it measures how unusual the statistic would be under a specified null model.
Can this replace a t-test or exact test?
No; it accepts a z statistic and standard normal reference only.