P-Value Calculator
Get one-tailed and two-tailed p-values for z-tests, t-tests and chi-square tests.
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Common test statistics and their p-values
Reference values worked out by this calculator. Your test is highlighted.
How p-values work
A p-value is the number most people look at first when they run a statistical test, and this calculator works it out from your test statistic in seconds. It is free, with no sign-up, and it runs entirely in your browser. It is made for students checking homework, teachers preparing lessons, and researchers who want a quick check before a full analysis.
What is a p-value?
A p-value is the probability of seeing a test result at least as extreme as yours if the null hypothesis were true. A small p-value means your result would be unusual under the null hypothesis, which is evidence against it. A large p-value means your result is ordinary under the null hypothesis, so there is little reason to doubt it.
What does a p-value of 0.05 mean?
A p-value of 0.05 means there is a 5 percent chance of getting a result this extreme if the null hypothesis were true. Researchers often treat 0.05 as a cut-off, calling results below it statistically significant. The cut-off is a convention, not a law of nature, and a p-value of 0.051 is barely different from 0.049 in practical terms.
How is a p-value calculated from a test statistic?
First you run a statistical test, which turns your data into a single number called a test statistic. Then you work out how likely that statistic, or one more extreme, is under the null hypothesis, using the matching distribution. A z-test uses the normal curve, a t-test uses the t distribution, and a chi-square test uses the chi-square distribution.
What is the difference between one-tailed and two-tailed p-values?
A one-tailed p-value looks in one direction only, asking whether the result is bigger than expected, or smaller, but not both. A two-tailed p-value looks in both directions and asks whether the result differs from the null in either direction. Two-tailed values are double the one-tailed value, and most research reports two-tailed p-values because they are the more cautious choice.
Does a small p-value prove the null hypothesis is false?
No, a small p-value never proves anything on its own. It only says the data would be surprising if the null hypothesis were true, which is not the same as proving the alternative. The American Statistical Association warned in 2016 that p-values are widely misused, and a single p-value should never decide a scientific question without context and replication.
Worked example
A z-test with a statistic of 1.96 gives a two-tailed p-value of 0.050, the classic boundary for significance. A t-test with a statistic of 2.0 and 10 degrees of freedom gives about 0.073, which is not significant at 0.05. A chi-square test with a statistic of 3.84 and 1 degree of freedom gives 0.050. Try each of these in the calculator above to see the one-tailed value too.
Why are chi-square tests one-sided?
Chi-square statistics are always zero or positive, because they are built from squared differences, so there is no left tail to test. A chi-square test only asks whether the statistic is unusually large, which is why the one-tailed and two-tailed values shown here are the same upper-tail probability. Textbooks such as OpenStax Introductory Statistics describe the chi-square test as a right-tailed test for this reason.
Frequently asked questions
What p-value is considered significant?
By convention, a p-value below 0.05 is called statistically significant, and a value below 0.01 is called highly significant. The 0.05 cut-off is a habit that dates back to the statistician Ronald Fisher in the 1920s, not a natural law, so always report the exact p-value alongside the verdict.
Can a p-value be greater than 1?
No. A p-value is a probability, so it always falls between 0 and 1. A value very close to 1 means your result is exactly what the null hypothesis would predict, while a value very close to 0 means it is almost impossible under the null.
What does p less than 0.001 mean?
It means there is less than a 0.1 percent chance of seeing a result this extreme if the null hypothesis were true. Such a small value is strong evidence against the null, but it still does not prove the alternative, and it says nothing about how large or important the effect is.
Is a two-tailed p-value always double the one-tailed value?
For z-tests and t-tests, yes, because the distributions are symmetric and the two-tailed value counts both tails. For chi-square tests, no, because the test is one-sided by nature, so this calculator shows the same upper-tail probability for both.
Why is my chi-square p-value the same one-tailed and two-tailed?
Chi-square statistics cannot be negative, so there is no second tail to add. The test only looks at the upper tail, asking whether the statistic is unusually large. Both values therefore report the same probability, which is the standard way to present a chi-square result.
What is the null hypothesis?
The null hypothesis is the default claim that there is no effect, no difference, or no relationship in your data. A test asks whether the data is surprising enough under that claim to doubt it. Rejecting the null does not prove the alternative claim, it only says the data fits the null poorly.
Does this calculator store my data?
No. The calculator runs entirely in your browser. Nothing you type is uploaded, stored or shared, and closing the page clears it.
More tools you may need
Working with a single value instead of a test statistic? Use our Z-Score Calculator. Need the spread of your data set first? Try our Standard Deviation Calculator.
