Free statistics tool
Free P-Value Calculator
Enter a z score, or a t score with its degrees of freedom, to get the p-value. Pick one-tailed or two-tailed and a significance level, and the calculator tells you if the result is significant.
Live calculator
Calculate a p-value
Two-tailed p-value
0.0357
Significant at α = 0.05: p is below 0.05.
What is a p-value?
A p-value answers one question: if there were really no difference, how often would you see a result at least as extreme as this one, just by chance? A small p-value means your result would be rare if nothing were going on, so it counts as evidence against "no difference".
Common misreadings to avoid:
- A p-value is not the chance that the result is a fluke. p = 0.03 does not mean a 3% chance you are wrong.
- It is not the chance that your variant is better. 1 - p is not "97% sure".
- It does not tell you how big the effect is. A tiny effect on a large sample can have a very small p-value.
- p = 0.06 is not "no effect". It means the data is not strong enough at your chosen level.
How to calculate a p-value from a z or t score
The test statistic (z or t) tells you how many standard errors your result is from zero. The p-value is the area in the tail of the distribution beyond that point.
From a z score: two-tailed p = 2 × (1 - Φ(|z|)), where Φ is the standard normal distribution. Example: z = 2.1. Φ(2.1) = 0.9821, so p = 2 × 0.0179 = 0.0357. That is below 0.05, so the result is significant at the 5% level.
From a t score: use the Student t distribution with your degrees of freedom instead of the normal. Example: t = 2.228 with 10 degrees of freedom gives a two-tailed p of 0.05. The same 2.228 as a z score would give p = 0.026, because the t distribution has fatter tails for small samples. As the degrees of freedom grow, t and z give the same answer. To turn raw data into a z score first, use the z-score calculator.
One-tailed vs two-tailed
A two-tailed test counts extreme results in both directions: better or worse. A one-tailed test only counts the direction you predicted, so its p-value is half the two-tailed one. This calculator measures the one-tailed p-value in the direction your statistic points. Choose one-tailed only if you decided on the direction before you saw the data. Switching to one-tailed after the fact to get under 0.05 is cheating yourself.
P-values in A/B testing
In an A/B test the p-value tells you how surprising the difference between control and variant would be if they really converted the same. To go straight from visitors and conversions to a p-value, use the A/B test significance calculator. For counts across more than two groups or categories, use the chi-square calculator.
Watch out for peeking. If you check the p-value every day and stop the first time it drops below 0.05, your real false positive rate is far higher than 5%. Decide the sample size up front with the sample size calculator, run the test until you reach it, and read the p-value once at the end.
FAQ
What does a p-value of 0.05 mean?
If there were really no difference, you would see a result at least this extreme 5% of the time. It does not mean there is a 5% chance the result is wrong or a 95% chance it is real.
Is a smaller p-value a bigger effect?
No. A p-value mixes effect size and sample size. A tiny lift on a huge sample can give a very small p-value. Look at the size of the difference and its confidence interval to judge if it matters.
Should I use a z score or a t score?
Use z when you know the population standard deviation or the sample is large, which is the case for most A/B tests on conversion rates. Use t with small samples where the standard deviation is estimated from the data.
When should I use a one-tailed test?
Only when you decided before looking at the data that you care about one direction, and a result in the other direction would lead to the same decision as no result. If in doubt, use two-tailed.
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