P-Value Calculator
Find the p-value from a z-score or t-score for a one- or two-tailed test. The chart shades the rejection area so you can see exactly what the p-value represents, with a clear significance decision.
Because p = 0.0500 < 0.05, you would reject the null hypothesis at the 5% level.
Standard normal distribution
p = 0.0500How to use this calculator
- Choose whether your test statistic is a z-score or a t-score.
- Enter the statistic (and the degrees of freedom for a t-score).
- Pick the tail of your test — two-tailed, left-tailed, or right-tailed.
- Read the p-value and the significance decision, and see the rejection area shaded on the chart.
What is a p-value?
The 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 result would be unlikely under the null hypothesis, which is evidence against it.
The shaded area under the curve in the chart above is the p-value: it is the tail probability beyond your test statistic (or beyond both ±|statistic| for a two-tailed test).
Z-score vs. t-score
Use a z-score when the population standard deviation is known or the sample is large; the p-value comes from the standard normal distribution. Use a t-score when the population standard deviation is unknown and estimated from the sample; the p-value comes from the Student’s t-distribution, which also needs the degrees of freedom.
As the degrees of freedom grow, the t-distribution approaches the standard normal, so the z and t p-values become nearly identical for large samples.One-tailed vs. two-tailed tests
- Two-tailed — tests for a difference in either direction; the p-value uses both tails.
- Right-tailed — tests whether the parameter is greater than the null value; the p-value uses the upper tail.
- Left-tailed — tests whether the parameter is less than the null value; the p-value uses the lower tail.
For a symmetric distribution, the two-tailed p-value is simply twice the one-tailed p-value for the same statistic.
How to interpret the p-value
Compare the p-value to your significance level (α), commonly 0.05. If the p-value is less than α, you reject the null hypothesis and call the result statistically significant. If it is greater than or equal to α, you fail to reject the null hypothesis.
A p-value is not the probability that the null hypothesis is true, and “not significant” does not prove the null hypothesis — it only means the evidence was not strong enough to reject it.P-value in Excel
For a z-score, a two-tailed p-value is =2*(1-NORM.S.DIST(ABS(z),TRUE)). For a t-score with df degrees of freedom, a two-tailed p-value is =T.DIST.2T(ABS(t),df), while =T.DIST.RT(t,df) gives the right-tailed p-value.
Frequently asked questions
What does a p-value of 0.05 mean?
A p-value of 0.05 means there is a 5% probability of observing a result at least as extreme as yours if the null hypothesis were true. It sits exactly at the common significance threshold, so it is the borderline between rejecting and not rejecting the null hypothesis at the 5% level.
Is a smaller p-value better?
A smaller p-value indicates stronger evidence against the null hypothesis. However, a small p-value does not measure the size or importance of an effect, only how incompatible the data is with the null hypothesis.
How do I convert a z-score to a p-value?
For a right-tailed test, the p-value is 1 minus the standard normal CDF of the z-score. For a two-tailed test, it is twice the tail area beyond the absolute value of the z-score. This calculator does the conversion for you.
When should I use a t-score instead of a z-score?
Use a t-score when the population standard deviation is unknown and estimated from your sample, which is the usual case for small samples. You also need the degrees of freedom, typically the sample size minus one.