📊 P-Value: Calculator

Get an exact p-value for Z-tests, T-tests, and Chi-Square tests.

P-VALUE
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two-tailed z-test
Significant at α=0.05?
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Significant at α=0.01?
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Enter a test statistic to compute the p-value.

What Is a P-Value?

A p-value is the probability of observing a test statistic at least as extreme as the one you calculated, assuming the null hypothesis is true. Smaller p-values indicate stronger evidence against the null hypothesis. This calculator computes exact p-values for the three most common hypothesis tests: the Z-test (known variance or large samples), the Student's t-test (small samples with estimated variance), and the Chi-Square test (variance and goodness-of-fit tests), using standard statistical distribution formulas rather than lookup-table approximations.

Z-test: p = 2 × (1 − Φ(|z|)) for a two-tailed test, where Φ is the standard normal CDF
T-test: p derived from the regularized incomplete beta function using the t-statistic and degrees of freedom
Chi-Square: p = 1 − P(k/2, χ²/2), the regularized lower incomplete gamma function

Choosing the Right Test

Use a Z-test when you know the population standard deviation or have a large sample size (generally n > 30). Use a T-test when working with a smaller sample and an estimated standard deviation — the t-distribution has heavier tails that account for that extra uncertainty, controlled by the degrees of freedom (typically sample size minus 1). Use a Chi-Square test for variance tests, goodness-of-fit tests, or tests of independence in categorical data.

One-Tailed vs. Two-Tailed Tests

A two-tailed test checks for a difference in either direction and is the more conservative, commonly used default. A one-tailed test only checks for a difference in one specific direction, which produces a smaller p-value for the same test statistic — use it only when your hypothesis specifically predicts the direction of the effect before you collect data.

📎 Related Tools: Z-Score Calculator Standard Deviation Calculator Confidence Interval Calculator Sample Size Calculator

❓ Frequently Asked Questions

What does it mean if my p-value is less than 0.05?
A p-value below 0.05 is the most common threshold for statistical significance, meaning there's less than a 5% probability of observing your result (or a more extreme one) if the null hypothesis were actually true. Many fields treat this as evidence to reject the null hypothesis, though 0.05 is a convention, not a universal law.
What's the difference between a Z-test and a T-test?
A Z-test assumes you know the population standard deviation (or have a large enough sample that the difference doesn't matter), while a T-test is used when the standard deviation is estimated from a smaller sample. The T-distribution has heavier tails than the normal distribution to account for that added uncertainty, and it requires degrees of freedom as an input.
How is the p-value calculated for a Chi-Square test?
It's calculated using the regularized lower incomplete gamma function, which gives the cumulative probability of the chi-square distribution up to your test statistic, with the degrees of freedom determining the shape of that distribution. This calculator implements the standard numerical method for that function rather than relying on a lookup table.
Should I use a one-tailed or two-tailed test?
Use a two-tailed test by default, since it checks for a difference in either direction and is more conservative. Only use a one-tailed test when your hypothesis specifically predicts the direction of the effect in advance, since it produces a smaller p-value for the same test statistic and shouldn't be chosen after seeing your data.
Does a small p-value prove my hypothesis is true?
No. A small p-value only indicates that your data would be unlikely under the null hypothesis — it doesn't prove your alternative hypothesis, measure the size of an effect, or account for issues like a poorly designed study or multiple comparisons.

🏆 About This Tool — Accuracy & Trust

🔒 Data Privacy: All calculations run entirely within your browser using JavaScript. Nothing you enter here is ever transmitted to our servers, stored, sold, or shared.

📐 Accuracy Note: This tool uses standard, widely published formulas and guidelines. Results are estimates for informational purposes; for financial, medical, or engineering decisions, consult a licensed professional.

📅 Last Updated: September 2026.