P-Value Calculator
Test Type
Tail
P-Value0.049996
Significant at 0.05?Yes
A p-value tells you how likely your observed test statistic would be if the null hypothesis were true. This calculator converts a z or t test statistic into a tail probability so you can decide whether a result is statistically significant. It uses a standard-normal approximation, so the same calculation is applied whether you label the input a z-score or a t-score.
Formula
p = 1 - normalCDF(|stat|), doubled for a two-tailed test
- stat
- Your test statistic (treated as a z-score)
- normalCDF
- Standard-normal cumulative distribution function
- p
- Resulting p-value, capped at a maximum of 1
How it works
- Enter your test statistic, then pick the test type (z-test or t-test) and the tail type (one-tail or two-tail). The engine uses a normal approximation, so the t-test and degrees-of-freedom inputs do not change the numeric result.
- The calculator takes the absolute value of your statistic and finds the upper-tail probability 1 - normalCDF(|stat|). For a two-tailed test that tail probability is doubled, and the final p-value is capped at 1.
- Compare the p-value to your significance level. This tool flags the result as significant when the p-value falls below 0.05.
Worked examples
A researcher obtains a z-statistic of 1.96 and runs a two-tailed test.
- Take the absolute value: |1.96| = 1.96.
- Find the upper tail: 1 - normalCDF(1.96) is about 0.025.
- Double it for two tails: 0.025 x 2 is about 0.05.
p ≈ 0.0500, which is right at the 0.05 threshold and flagged as significant.
An analyst has a z-statistic of 1.645 and runs a one-tailed test.
- Take the absolute value: |1.645| = 1.645.
- Find the upper tail: 1 - normalCDF(1.645) is about 0.05.
- No doubling is applied for a one-tailed test.
p ≈ 0.0500, sitting at the conventional one-sided significance boundary.
Frequently asked questions
- Does this calculator use the t-distribution for t-tests?
- No. This tool applies a standard-normal approximation to every statistic, so the z-test and t-test options return the same p-value. For small samples the true t-distribution gives a slightly larger p-value, so treat borderline t-test results with caution.
- What is the difference between a one-tailed and a two-tailed p-value?
- A one-tailed p-value measures the probability in a single direction, while a two-tailed p-value covers both tails and is simply double the one-tailed value here. Use two-tailed unless your hypothesis specifies a direction in advance.
- What p-value counts as statistically significant?
- This calculator marks a result significant when the p-value is below 0.05, the most common convention. Stricter fields may use 0.01 or 0.001, so always interpret the number against the threshold chosen before the experiment.
- Does the degrees of freedom field change the answer?
- No. Because the engine uses a normal approximation rather than an exact t-distribution, the degrees-of-freedom input does not affect the computed p-value. It is retained only as a label for your test setup.