Find the p-value of a test statistic and the critical value.
The p-value is the probability of a result at least as extreme as yours if the null hypothesis is true. A z-score of 1.96 (two-tailed) gives p = 0.0499958 — right at the 0.05 threshold.
A p-value measures the evidence against a null hypothesis: the smaller it is, the stronger the evidence. Choose the distribution of your test statistic — z, t, chi-square or F — enter its value and degrees of freedom, and pick a left, right or two-tailed test; the calculator returns the p-value and tells you whether the result is significant at your α. A second tool finds the critical value for any α.
Compute the statistic first with the Z-Score Calculator, Standard Deviation Calculator or Statistics Calculator. See also the Confidence Interval Calculator and Sample Size Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Test statistic | z (standard normal) = 1.96 |
| Left-tail probability | 0.9750021 |
| Right-tail probability | 0.024997895 |
| p-value (two-tailed) | 0.04999579 |
| Significance level α | 0.05 |
| Decision | Reject H₀ |
| Statistic | p-value |
|---|---|
| z = 1.0 | 0.317311 |
| z = 1.645 (right) | 0.0499849 |
| z = 1.96 | 0.0499958 |
| z = 2.576 | 0.00999506 |
| z = 3.0 | 0.0026998 |
| z | Area to the left Φ(z) | Area to the right | Two-tailed p |
|---|---|---|---|
| 0 | 0.5000 | 0.5000 | 1.0000 |
| 0.5 | 0.6915 | 0.3085 | 0.6171 |
| 1 | 0.8413 | 0.1587 | 0.3173 |
| 1.5 | 0.9332 | 0.0668 | 0.1336 |
| 1.645 | 0.9500 | 0.0500 | 0.1000 |
| 1.96 | 0.9750 | 0.0250 | 0.0500 |
| 2 | 0.9772 | 0.0228 | 0.0455 |
| 2.326 | 0.9900 | 0.0100 | 0.0200 |
| 2.576 | 0.9950 | 0.0050 | 0.0100 |
| 3 | 0.9987 | 0.0013 | 0.0027 |
| Degrees of freedom | 95% (α = 0.05) | 99% (α = 0.01) |
|---|---|---|
| 1 | 12.7062 | 63.6567 |
| 2 | 4.3027 | 9.9248 |
| 5 | 2.5706 | 4.0321 |
| 10 | 2.2281 | 3.1693 |
| 20 | 2.0860 | 2.8453 |
| 30 | 2.0423 | 2.7500 |
| 60 | 2.0003 | 2.6603 |
| 120 | 1.9799 | 2.6174 |
| ∞ (z) | 1.9600 | 2.5758 |
The probability, assuming the null hypothesis is true, of getting a result at least as extreme as the one observed.
By convention p < 0.05 is called statistically significant, but the threshold α should be chosen before the test.
A two-tailed test looks for a difference in either direction; a one-tailed test only one direction.
Find the area in the tail(s) beyond z: for z = 1.96 the two-tailed p-value is 0.05.
The number of independent values that can vary: for a one-sample t-test, n − 1.
No. It only says the result is unlikely under the null hypothesis — also look at the effect size and confidence interval.
It uses the standard method: two-tailed p = 2 × min(CDF, 1 − CDF) reject H₀ if p < α The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
