P-Value Calculator

Enter a z-score to find the corresponding p-value, one-tailed or two-tailed.

P-Value Calculator

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Z-score

Test type

P-value

0.0316

Significant at α=0.05?

Yes

Significant at α=0.01?

Assumes a standard normal (z) distribution. For small sample sizes, a t-distribution may be more appropriate.

The formula

One-tailed p-value = 1 - CDF(|z|) Two-tailed p-value = 2 x (1 - CDF(|z|))

Example

A z-score of 2.15, two-tailed test: p-value = 2 x (1 - 0.9842) ≈ 0.0316 - significant at the common α=0.05 threshold, but not at α=0.01.

Step-by-step guide

Enter your z-score - use our Z-Score Calculator first if you need to compute it from raw data.
Choose one-tailed or two-tailed, based on your hypothesis (whether you're testing for a difference in a specific direction, or any difference at all).
Read the p-value and compare it against your significance threshold.

What a p-value actually means (and what it doesn't)

A p-value estimates the probability of seeing a result at least as extreme as yours, purely by chance, if there were truly no real effect (the "null hypothesis"). A small p-value suggests your result would be unusual under that assumption, which is why it's often used as evidence against the null hypothesis - but a p-value is not the probability that the null hypothesis is true, and a "significant" result isn't automatically a large or important one. It's one piece of evidence, not a final verdict.

Common mistakes

Interpreting p < 0.05 as "there's a 95% chance the effect is real" - a p-value describes how surprising the data would be under the null hypothesis, not the probability that a hypothesis is true.

Using a two-tailed test when your hypothesis is actually directional (or vice versa) - this choice should be decided before looking at your data, based on what you're actually testing.

Frequently asked questions

What's the difference between one-tailed and two-tailed?

A one-tailed test checks for an effect in one specific direction only (like "is the new method better," not just "different"). A two-tailed test checks for a difference in either direction, which is why it produces a larger p-value for the same z-score.

What significance level should I use?

0.05 is the most commonly used threshold across many fields, though some contexts (like certain medical or physics research) use a stricter 0.01 or even smaller - the right choice depends on your specific field's conventions and how costly a false positive would be.

Should I use a z-score or t-score for my p-value?

A z-score is appropriate with a large sample size or known population standard deviation; a t-distribution is more accurate for smaller samples with an estimated standard deviation, and produces a slightly different (generally larger) p-value for the same test statistic.

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