Math & Statistics
P-Value Calculator for a Z Test
Approximate one-tailed and two-tailed p-values from a z test statistic using the standard normal distribution. The calculator uses two-tailed p = 2 × (1 − Φ(|z|)). It returns more than one result so you can check the main answer against a useful secondary measure. A smaller p-value means the observed statistic is less compatible with the null model, not that the null has a specific probability. A p-value does not measure effect size, practical importance, study quality, or the probability that a hypothesis is true.
Check the displayed units, assumptions, and rounding before relying on the result.
Calculate and compare
Use the number box for precision or the slider for fast scenario testing.
Scenario results
Two-tailed p-value
0.035729
Below entered alpha.
One-tailed p-value
0.017864
Tail in the observed direction.
Decision comparison
Reject by threshold
A mechanical comparison, not a scientific conclusion.
How the calculation works
Use consistent units and retain full precision until the final display step.
Worked example
Reproduce the displayed scenario, then change one assumption at a time.
Assumptions behind the result
- • Inputs use the units shown beside each control.
- • The displayed formula is applied without hidden market or demographic data.
- • Rounding occurs only for display; calculations keep full numeric precision.
- • A smaller p-value means the observed statistic is less compatible with the null model, not that the null has a specific probability.
- • A p-value does not measure effect size, practical importance, study quality, or the probability that a hypothesis is true.
Mistakes that change the answer
- • Mixing percentages with decimals or mixing incompatible units.
- • Relying on a rounded intermediate value instead of the full result.
- • Changing several assumptions at once instead of testing z statistic separately.