P Value Calculator

A p-value tells you how likely your data (or something more extreme) would be if there were no real effect — the smaller the p-value, the stronger the evidence against that assumption. This p value calculator converts a test statistic into a p-value for the z or Student-t distribution, using whichever tail you choose.

How to use this calculator

1. Enter your test statistic — the z-score or t-value from your test (default 1.96).
2. Choose the distribution: z for a known population standard deviation or a large sample, Student-t for a small sample with an estimated standard deviation.
3. If you picked Student-t, enter the degrees of freedom (default 10) — this is not used for the z distribution.
4. Choose the tail: left, right, or two-sided, matching how your hypothesis test is set up.

Worked example

Take the default inputs: a z distribution, test statistic 1.96, and a two-sided tail. This is how to find p value from a test statistic step by step.

First, find the area to the left of 1.96 under the standard normal curve:

Φ(1.96) ≈ 0.9750

The area in the upper tail is what’s left over:

right tail p = 1 − 0.9750 = 0.0250

For a two-sided test, double the tail:

two-sided p = 2 × 0.0250 = 0.0500

So z = 1.96 gives a two-sided p-value of about 0.05 — a widely used reference point in hypothesis testing. If you only cared about one side of the distribution, you’d stop at the single-tail value: 0.025. See the NIST/SEMATECH e-Handbook on hypothesis testing for the general procedure this calculator follows.

Frequently asked questions

What counts as statistically significant?

A result is usually called statistically significant when the p-value falls below a chosen significance level, commonly 0.05. That threshold is a convention, not a law of nature — some fields use 0.01 for stricter evidence or 0.10 for exploratory work.

Should I use a one-tailed or two-tailed p-value?

Use a two-sided tail when you only care whether the result differs from the expected value in either direction; use a one-sided (left or right) tail when your hypothesis specifically predicts the direction of the effect before you collect data.

When should I use the Student-t distribution instead of z?

Use Student-t with the matching degrees of freedom when your sample is small and you estimated the standard deviation from the data itself; use z when the population standard deviation is known or your sample is large enough that the two distributions nearly coincide.

Does a small p-value prove my hypothesis is true?

No. A p value from test statistic only measures how surprising your data would be under the assumption of no effect — it doesn’t measure the size of the effect or prove any hypothesis, and it should be interpreted alongside effect size and study design.