P Value Calculator
Convert a z-score into a p-value for left, right or two-tailed tests. Free p-value calculator with a hypothesis-test decision against your significance level.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the steps
How the P Value Calculator Works
Enter a z-score (your standardized test statistic), choose the tail of the test, and set your significance level α. The calculator returns the p-value from the standard normal distribution and tells you whether to reject or fail to reject the null hypothesis.
The Method
The p-value is an area under the standard normal curve, computed from the cumulative distribution function (CDF):
Left-tailed: p = P(Z < z) Right-tailed: p = P(Z > z) Two-tailed: p = 2 × P(Z > |z|)
You then compare p to your chosen α. If p < α, the result is statistically significant.
Worked Example
Suppose your test gives z = 1.96 and you run a two-tailed test at α = 0.05:
- The area beyond |z| = 1.96 in one tail is about 0.025.
- Two-tailed p-value = 2 × 0.025 = 0.05.
- Since p is not below α (it equals it), this is the classic borderline case — any z beyond ±1.96 gives p < 0.05 and rejects the null.
Common Z-Scores and Two-Tailed P-Values
| Z-score | Two-tailed p-value | Significant at 0.05? |
|---|---|---|
| 1.00 | 0.317 | No |
| 1.645 | 0.100 | No |
| 1.96 | 0.050 | Borderline |
| 2.576 | 0.010 | Yes |
Reading the Result Correctly
A p-value answers one narrow question: how surprising is this data if the null hypothesis is true? It does not measure the size of an effect or the probability that the null is true. Pair the p-value with an effect size and confidence interval, and decide α before you collect data to keep the test honest.
Frequently asked questions
What is a p-value?+
A p-value is the probability of observing a test statistic at least as extreme as the one you got, assuming the null hypothesis is true. A small p-value means your data would be unlikely under the null hypothesis, which is evidence against it.
How do you convert a z-score to a p-value?+
Use the standard normal distribution. For a right-tailed test the p-value is the area above your z-score; for a left-tailed test it is the area below it; for a two-tailed test it is twice the area beyond the absolute value of z. This calculator does all three automatically.
What does it mean if the p-value is less than 0.05?+
If the p-value is below your significance level (commonly 0.05), the result is statistically significant and you reject the null hypothesis. A p-value of 0.03, for example, means there is only a 3% chance of seeing data this extreme if the null hypothesis were true.
What is the difference between a one-tailed and two-tailed test?+
A one-tailed test checks for an effect in a single direction (greater than or less than), putting the whole rejection region in one tail. A two-tailed test checks for any difference in either direction and splits the region between both tails, which roughly doubles the p-value for the same z-score.
Does a non-significant p-value prove the null hypothesis?+
No. Failing to reject the null hypothesis means you do not have enough evidence against it, not that it is true. A large p-value can also result from a small sample or low statistical power, so absence of significance is not proof of no effect.