P-Value Calculator (from Z)
Convert a z-score to a one- or two-tailed p-value.
Results update as you type.
About this calculator
This p-value calculator converts a z-score (the standard-normal test statistic) into a p-value — the probability of observing a result at least as extreme as yours if the null hypothesis is true. A small p-value means your data would be surprising under the null hypothesis, which counts as evidence against it.
Choose a left-tailed, right-tailed or two-tailed test; all three p-values are shown so you can compare. The left-tailed value is P(Z ≤ z), the right-tailed value is P(Z ≥ z), and the two-tailed value is 2 × P(Z ≥ |z|) — double the smaller tail. All come from the standard-normal cumulative distribution, so this tool applies to z-tests and large-sample approximations, and the result is flagged against the conventional α = 0.05 threshold.
Worked example: a z-score of 1.96 gives a right-tailed p-value of about 0.025 and a two-tailed p-value of about 0.050 — exactly the classic 5% cutoff, which is why 1.96 is the critical value for a 95% two-sided test. Since 0.05 is not below 0.05, that result sits right on the border of significance.
Frequently asked questions
What is a p-value?
The p-value is the probability, assuming the null hypothesis is true, of getting a test statistic at least as extreme as the one observed. A small p-value means your data would be unlikely under the null hypothesis, which is evidence against it.
How does a two-tailed p-value differ from one-tailed?
A two-tailed test counts extreme results in both directions, so its p-value is double the one-tailed value for the same |z|. Use two-tailed when you only care that there is a difference, and one-tailed when you predicted the direction in advance.
Is p < 0.05 always significant?
0.05 is only a common convention, not a law. It means a 5% chance of a false positive. Depending on the field and the cost of being wrong, stricter thresholds like 0.01 are often more appropriate.
How do I convert a z-score to a p-value?
Look up the tail area of the standard-normal distribution beyond your z-score. This tool does it for you: the left tail is P(Z ≤ z), the right tail is 1 − P(Z ≤ z), and the two-tailed p-value doubles the smaller of the two.
Does a large p-value prove the null hypothesis is true?
No. A large p-value only means your data is consistent with the null hypothesis, not that the null is proven. Absence of evidence against it is not evidence for it; you may simply lack the sample size to detect an effect.
When should I use a z-based p-value instead of a t-based one?
Use the z-based value when the population standard deviation is known or the sample is large (roughly n ≥ 30). For small samples with an estimated standard deviation, a t-distribution gives a more accurate p-value.
What is the difference between the p-value and the significance level?
The significance level α is a threshold you set in advance, such as 0.05. The p-value is computed from your data. You reject the null hypothesis when the p-value falls below α.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/p-value/curl
curl "https://calculator.free/api/v1/p-value/?z=1.96&tail=two"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/p-value/?" + new URLSearchParams({
"z": "1.96",
"tail": "two"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.