WorldCalcs

P-value Calculator

Turn a z-score or t-score into a p-value for one- or two-tailed hypothesis tests.

Reviewed by the WorldCalcs team · Methodology · Last reviewed: July 2026

p-value

0.0500

At α = 0.05, this result is statistically significant.

What is a p-value?

A p-value measures how surprising your data would be if the null hypothesis were true. A small p-value means results like yours would rarely happen by chance alone, which is evidence against the null hypothesis. This calculator converts a test statistic — either a z-score or a t-score — into a p-value for a one- or two-tailed test, so you can compare it against your chosen significance level. To find the underlying test statistic first, use the z-score calculator.

How the p-value is calculated

The p-value is the tail area of a probability distribution beyond your test statistic. A z-score uses the standard normal distribution; a t-score uses Student's t-distribution with your degrees of freedom, which has heavier tails for small samples. A two-tailed test measures both tails, so its p-value is 2 × P(Z ≥ |z|). A right-tailed test uses P(Z ≥ z), and a left-tailed test uses P(Z ≤ z). You then compare the p-value with your significance level α — often 0.05 — to decide whether the result is statistically significant. Pair this with the confidence interval calculator and the standard deviation calculator when reporting results.

Example

A two-tailed z-test with z = 1.96 gives a p-value of about 0.0500, sitting right on the classic 0.05 threshold. Switching to a t-test with t = 2.131 and 15 degrees of freedom also gives roughly 0.0500 — the t-distribution needs a slightly larger statistic to reach the same p-value because its tails are heavier.

All calculations happen in your browser. Nothing is sent, stored, or tracked.

Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer

How to use

Choose whether your statistic is a z-score or a t-score, enter its value (may be negative), pick the tail of the test, and — for t-scores — enter the degrees of freedom. The calculator returns the p-value and states whether the result is significant at α = 0.05.

Use two-tailed when you're testing for any difference; use one-tailed only when a directional hypothesis was set in advance.

Frequently asked questions

What is a p-value in plain terms?+

It's the probability of seeing a result at least as extreme as yours if the null hypothesis were true. Smaller p-values mean your data is less compatible with the null hypothesis.

What does a p-value of 0.05 mean?+

It means there's roughly a 5% chance of observing a result this extreme purely by chance under the null hypothesis. Many fields treat 0.05 as the cutoff for statistically significant, but it's a convention, not a law.

Should I use a one-tailed or two-tailed test?+

Use two-tailed when you're testing for any difference in either direction — this is the safe default. Use one-tailed only when you have a specific directional hypothesis decided in advance.

How do I get a p-value from a z-score?+

Find the area in the tail beyond your z-score on the standard normal curve. For a two-tailed test, double that tail area. This calculator does it automatically.

When should I use a t-score instead of a z-score?+

Use a t-score when the sample is small and the population standard deviation is unknown — the t-distribution accounts for that extra uncertainty through its degrees of freedom.

What are degrees of freedom?+

For a one-sample t-test, degrees of freedom equal the sample size minus one. They control the exact shape of the t-distribution; more degrees of freedom make it look more like the normal curve.

Does a small p-value prove my hypothesis?+

No. A small p-value is evidence against the null hypothesis, but it doesn't measure the size or importance of an effect, and it can't prove the alternative is true.

What p-value is considered statistically significant?+

Conventionally, a p-value below 0.05 is called significant, with 0.01 and 0.001 used as stricter thresholds. The right cutoff depends on your field and the cost of a wrong conclusion.

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