Enter your test statistic (z-score) and choose the test type — two-tailed, left-tailed, or right-tailed. You'll get the p-value and whether it's statistically significant at the 0.05 and 0.01 levels.
How the p-value calculator works
A p-value answers a very specific question: if the null hypothesis were true, how often would random chance alone produce a result at least this extreme? The calculator takes your z-score and measures the tail area of the standard normal distribution beyond it. A two-tailed test counts extremes in both directions; a one-tailed test counts only the direction you predicted in advance.
The formula
Two-tailed: p = 2 × (1 − Φ(|z|))
Left-tailed: p = Φ(z) Right-tailed: p = 1 − Φ(z)
Here Φ(z) is the standard normal cumulative distribution function — the share of the distribution at or below z — and |z| is the absolute value of your z-score.
Worked example
Your A/B test produces a z-score of 2.5, and you're running a two-tailed test:
Φ(2.5) ≈ 0.9938, so the upper tail is 1 − 0.9938 = 0.0062. Doubling for both tails:
p = 2 × 0.0062 = 0.0124
That's significant at α = 0.05 (0.0124 < 0.05) but not at α = 0.01 (0.0124 > 0.01). A result this extreme would occur by chance about 1.2% of the time under the null.
What a p-value is not
The single most common misreading: a p-value of 0.0124 does not mean there's a 1.24% chance the null hypothesis is true, and it does not mean a 98.76% chance your effect is real. The p-value is computed assuming the null is true — it can't turn around and tell you the probability of that assumption. It also says nothing about the size or importance of an effect: with a huge sample, a difference too small to matter can still produce p < 0.001. Read a p-value as a measure of surprise under the null, then look at the effect size and confidence interval to decide whether the finding actually matters.
Frequently asked questions
What is a p-value in simple terms?
It's the probability of seeing data at least as extreme as yours if the null hypothesis were true. A small p-value says "this result would be surprising under the null," which counts as evidence against it. It is not the probability that the null hypothesis is true.
Is p = 0.05 significant?
The usual convention requires the p-value to be below the threshold, so p = 0.05 exactly does not clear α = 0.05. In practice, results that close to the line deserve skepticism either way — the difference between p = 0.049 and p = 0.051 is scientifically meaningless.
When do I use a two-tailed vs. a one-tailed test?
Use two-tailed when a difference in either direction would matter (the default in most research). Use a one-tailed test only when you specified the direction before collecting data and the opposite direction is genuinely irrelevant. Choosing one-tailed after seeing the data — to halve your p-value — is a classic form of p-hacking.
How do I get a z-score to put into this calculator?
A z-test statistic is typically (sample mean − hypothesized mean) ÷ standard error, where the standard error is the population standard deviation divided by √n. Many software outputs report the z (or t) statistic directly. For large samples, a t-statistic is approximately a z-score.
Does a small p-value mean the effect is large or important?
No. With a big enough sample, even a trivially tiny effect produces a tiny p-value. Statistical significance says an effect is probably not zero; it says nothing about whether it's big enough to care about. Always look at the effect size and confidence interval alongside the p-value.