P-value Calculator
Press Calculate to see the results.
This p-value calculator converts a z-score into the left-tail, right-tail, two-tailed and central probabilities of the standard normal distribution, or works backward from any one p-value to the z-score.
Enter a z-score and leave the other boxes empty to see all five probabilities at once, or clear the z-score and enter a single p-value to find the z-score that produces it. The default, z = 2, has a two-tailed p-value of about 0.0455 and a right-tail p-value of about 0.0228.
In hypothesis testing, the p-value is the probability of getting a result at least as extreme as the one observed, assuming the null hypothesis is true. It is not the probability that the null hypothesis is true, and it does not measure how large or important an effect is. A small p-value says only that the data would be surprising if the null hypothesis held.
Choosing the tail depends on the alternative hypothesis. A right-tailed test asks whether a value is larger than expected, so its p-value is P(Z > z). A left-tailed test asks whether it is smaller, using P(Z < z). A two-tailed test looks for a difference in either direction and doubles the smaller tail, P(Z < −|z| or Z > |z|). Decide which test you are running before looking at the data; switching to a one-tailed test after the fact halves the p-value and overstates the evidence.
The result is compared with a significance level α chosen in advance, most often 0.05. If the p-value is at or below α, the result is called statistically significant and the null hypothesis is rejected. For a two-tailed test at α = 0.05, that happens when |z| is at least 1.96. Other common cut-offs are 0.10, 0.01 and 0.001.
This calculator covers z statistics, which apply when the population standard deviation is known or the sample is large, and to tests of proportions. Tests based on the t, chi-square or F distributions use the same tail logic but different curves, so their p-values for the same statistic differ, especially with small samples.
The American Statistical Association has cautioned against treating 0.05 as a bright line. Report the exact p-value with an effect size and a confidence interval, and remember that a non-significant result is not proof that there is no effect.
Frequently asked questions
How do I get a p-value from a z-score?
Find the area under the standard normal curve beyond z. For a right-tailed test it is 1 − Φ(z); for a two-tailed test it is 2 × (1 − Φ(|z|)).
What is the p-value for z = 1.96?
The two-tailed p-value is 0.05 and the right-tail p-value is 0.025.
Is a smaller p-value better?
A smaller p-value means stronger evidence against the null hypothesis, but it says nothing about the size or practical importance of the effect.
When should I use a two-tailed test?
Use it when you care about a difference in either direction, which is the usual default in research.
Can I find the z-score from a p-value?
Yes. Clear the z-score box, enter the p-value in the matching tail box, and the calculator returns the z-score.
How do I get a p-value from a t-statistic?
Use the t-distribution with the right degrees of freedom, usually n − 1 for a one-sample t-test, instead of the normal curve. With 10 degrees of freedom, t = 2.228 has a two-tailed p-value of 0.05, while the same value treated as a z-score gives about 0.026. This calculator uses the normal distribution, so it matches t-test results only for large samples, where the two curves are nearly identical.
Updated by Calculator.hair. How we build and check our calculators