P-value calculator from a z statistic
Enter a z statistic and choose the alternative direction. HitEquals returns the p-value, both one-sided tail areas, the central area and common alpha comparisons.
Inputs used by this calculator
P-value Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Z statistic | 1.96 | -38 to 38 | Supplies the z statistic quantity used by the published equation or result breakdown. |
| Alternative hypothesis | Two-sided | Two-sided · Left-tailed · Right-tailed | Supplies the alternative hypothesis quantity used by the published equation or result breakdown. |
What a p-value represents
A p-value is the probability, under the specified null model, of a test statistic at least as extreme in the direction defined by the alternative.
One-sided alternatives
A left-tailed alternative uses the cumulative area Φ(z). A right-tailed alternative uses one minus that area.
Two-sided alternative
For a symmetric standard normal, double the smaller tail area.
p=2·min(Φ(z),1−Φ(z))Worked z=1.96 example
The right-tail area beyond 1.96 is about 0.025. Doubling it gives a two-sided p-value near 0.05.
P-value is not effect size
A small p-value does not show practical importance, causality or the probability that the null hypothesis is true. Report estimates and intervals with the test.
Test-selection limits
This page assumes the input already follows a standard normal null distribution. Estimated variance, small samples, discrete tests and dependent data may require a different reference distribution.
Common two-sided z landmarks
| |z| | Two-sided p |
|---|---|
| 1.645 | ≈0.10 |
| 1.960 | ≈0.05 |
| 2.576 | ≈0.01 |
| 3.291 | ≈0.001 |
Frequently asked questions
What does p=0.05 mean?
Under the null model, results at least this extreme have about a 5% probability under the stated alternative.
Is p the probability the null is true?
No.
When is a test two-sided?
When departures in either direction count as evidence.
Can a p-value exceed one?
No.
Does statistical significance imply importance?
No. Examine effect size and uncertainty.
Can I enter a t statistic?
No. This page uses the standard normal distribution only.
What to keep in mind
This converts an already valid z statistic under a standard-normal null model. It does not choose a test, verify assumptions, adjust multiple comparisons or calculate a t, chi-square or F p-value.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.