Free p-value calculator
Calculate the p-value from a z-score or t-statistic — enter your test statistic and pick one-tailed or two-tailed to see the probability, updated live, as you type.
On this page10 sections
Two-tailed p-value from z-test. Uses approximation of the standard normal CDF.
Results are estimates. Consult a professional.
How the p-value calculator works
A p-value is the probability of observing a test statistic at least as extreme as the one measured, assuming the null hypothesis (H₀) is true. The smaller the p-value, the stronger the evidence against H₀. This calculator computes p-values for z-tests and t-tests in one-tailed or two-tailed form.
Worked example: two-tailed z-test
A researcher tests whether a new drug changes blood pressure. The computed z-score is 2.5. Using a two-tailed test at α = 0.05, should they reject the null hypothesis?
Z-scores and p-values for common significance levels
This table shows the critical z-scores and corresponding two-tailed p-values for the significance levels researchers most often use.
| Significance level (α) | Critical z-score (two-tailed) | p-value at critical z |
|---|---|---|
| 0.10 (10%) | ±1.645 | 0.1000 |
| 0.05 (5%) | ±1.960 | 0.0500 |
| 0.01 (1%) | ±2.576 | 0.0100 |
| 0.001 (0.1%) | ±3.291 | 0.0010 |
Source: Standard normal distribution tables. Two-tailed p-values shown; halve for one-tailed tests.
Tips for using p-values correctly
P-values are widely used but frequently misunderstood. These tips help you interpret and report them accurately.
- p < α does not prove the effect is large — statistical significance and practical significance are different things; always report effect size alongside the p-value.
- Decide on α before running the test — choosing a threshold after seeing the data (p-hacking) inflates the false-positive rate; 0.05 is conventional but not sacred.
- One-tailed vs. two-tailed — use a one-tailed test only when you have a strong prior reason to expect the effect in one direction; two-tailed is the safer default.
- p > α does not prove H₀ is true — a non-significant result means insufficient evidence to reject H₀, not proof that no effect exists.
- Sample size matters — with very large samples, tiny and practically meaningless differences become statistically significant; with small samples, real effects may not reach significance.
Accuracy and limitations
P-values computed here assume the test statistic follows a standard normal (z) or t-distribution. The validity of those assumptions depends on your data: the z-test requires either a known population standard deviation or a large sample (n ≥ 30 by the central limit theorem). For small samples with unknown variance, use the t-distribution. This calculator does not account for multiple comparisons — if you run many tests simultaneously, apply a correction such as Bonferroni or Benjamini-Hochberg to control the family-wise error rate.
Key terms
About this calculator
Part of our math calculators suite — explore all calculators.