P-value calculator.
Turn a test statistic into a p-value. Enter a z-score or t-score, choose the distribution and the tail, and the calculator returns the p-value.
Test statistic
LiveFor a z-score the calculator uses the standard normal distribution; for a t-score it uses the Student t-distribution with the degrees of freedom you enter.
P-value
0.05000
two-tailed, normal
Assumes a valid test statistic from a properly specified test. Calculations run in your browser; nothing you enter is stored.
How it works
Statistic to probability
A p-value is the probability of getting a test statistic at least as extreme as the one you observed, if the null hypothesis were true. Small p-values cast doubt on the null hypothesis.
For a z-score the calculator reads the probability off the standard normal curve; for a t-score it uses the t-distribution, which is a little wider and depends on the degrees of freedom. A two-tailed test counts both extremes, a one-tailed test only one.
Reference
Z-score to p-value.
Two-tailed p-values for common z-scores from the standard normal distribution.
| Z-score | Two-tailed p |
|---|---|
| 1.000 | 0.3173 |
| 1.282 | 0.1998 |
| 1.645 | 0.1000 |
| 1.960 | 0.0500 |
| 2.576 | 0.0100 |
| 3.291 | 0.0010 |
The full guide
The complete guide to p-values.
What a p-value is, how tails and distributions change it, and how to read significance.
What a p-value is
A p-value answers a single question: if nothing real were going on, how often would you see a result at least this extreme by chance? It runs from 0 to 1, and the smaller it is, the more surprising your data is under the null hypothesis.
It is not the probability that the null hypothesis is true, and it does not measure effect size, only how unusual the statistic is.
One-tailed versus two-tailed
A two-tailed test asks whether the statistic is extreme in either direction, so it counts both tails of the curve. A one-tailed test looks in a single pre-chosen direction and so gives a p-value half the size for the same statistic.
Choose the tail before you see the data, based on your hypothesis, not afterwards to get a smaller number.
Normal versus t-distribution
Use the normal (z) distribution when the standard deviation is known or the sample is large. Use the t-distribution for smaller samples with an estimated standard deviation; it has heavier tails, so it gives slightly larger p-values, and it converges on the normal as degrees of freedom grow.
Enter the degrees of freedom for a t-test, typically the sample size minus one.
Reading significance
Researchers often compare the p-value to a threshold, alpha, commonly 0.05. Below it, the result is called statistically significant; above it, it is not. A z of 1.96 sits right at the two-tailed 0.05 boundary.
Significance is not importance: always report the effect size and confidence interval alongside the p-value.
The formula
Statistic
to p.
For a z-score the two-tailed p-value is erfc of the absolute z over the square root of two; for a t-score it uses the t-distribution with your degrees of freedom.
Chi-square test ›# From a z-score
two-tailed p = erfc( |z| / sqrt(2) )
one-tailed p = p_two / 2
# example
z = 1.96 → p = 0.0500Questions
P-value questions.
How do I find a p-value from a z-score?
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For a two-tailed test, the p-value is erfc of the absolute z-score divided by the square root of two; for one-tailed, halve it. Enter your z-score above and the calculator does it.
What does a p-value of 0.05 mean?
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It means a result this extreme would happen about 5% of the time by chance if the null hypothesis were true. Many fields treat 0.05 as the threshold for significance.
When should I use the t-distribution?
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Use the t-distribution for smaller samples where the standard deviation is estimated from the data. Choose t above and enter the degrees of freedom, usually the sample size minus one.
Is a smaller p-value better?
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A smaller p-value means stronger evidence against the null hypothesis, but it does not measure how large or important the effect is. Always report effect size too.
Is this p-value calculator free?
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Yes. It is completely free with no sign-up, and every calculation runs locally in your browser, so nothing you enter is stored or sent anywhere.
About the developer
Jean Borg
Jean builds and maintains every calculator on freecalculators.pro from Malta, with a focus on tools that are fast, free and show their working. The p-value calculator uses standard normal and t-distribution functions for accurate tail probabilities.