P-Value Calculator
Find the p-value for z, t and chi-square test statistics with one or two tails. Decide significance at the 5% level instantly.
p-value
0.05
Two-tailed
Significance
Statistically significant
At the 5% level
A p-value below 0.05 is conventionally taken as evidence against the null hypothesis.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Use the p-value calculator whenever a study, experiment or analysis produces a test statistic and you need to judge statistical significance — the standard step in dissertations, journal papers, clinical trials and Six Sigma projects across India. It converts z-scores, t-scores and chi-square statistics into p-values using the exact underlying distributions, so you never need printed tables that only list a handful of cutoff values. Researchers in agriculture, medicine and economics use it to decide whether observed differences are real or plausibly due to chance, while quality engineers apply it to process improvement experiments. The one-tailed and two-tailed toggle matches the two hypothesis styles used in practice, and the automatic comparison with the 5% threshold gives an immediate, clearly worded significance verdict alongside the exact p-value.
How to Use This Calculator
- Step 1: Choose the type of test statistic — z, t or chi-square.
- Step 2: Enter the computed statistic value from your test, such as 1.96 for a z-test.
- Step 3: For t and chi-square tests, enter the degrees of freedom from your study.
- Step 4: Choose one-tailed or two-tailed, then read the p-value and the 5% significance verdict.
Worked Example
A pharmaceutical lab in Hyderabad runs a two-tailed z-test comparing a new formulation with a standard one and obtains z = 1.96. Enter the z option with value 1.96 and two-tailed: the p-value is 0.0500, exactly at the conventional threshold, so the difference is borderline significant. For a t-test with 10 degrees of freedom and t = 2.228 the two-tailed p-value is also 0.0500 — the two statistics reach the same conclusion at different values because they come from different distributions.
Tips and Common Mistakes
- •Tip 1: Decide one-tailed versus two-tailed before collecting data; switching afterwards is considered p-hacking.
- •Tip 2: For small p-values below 0.0001 the calculator shows '< 0.0001', which is the standard way journals report them.
- •Tip 3: Report the exact p-value alongside the significance verdict rather than just saying significant or not.
- ✗Mistake 1: Interpreting the p-value as the probability that your hypothesis is true — it only assumes the null is true.
- ✗Mistake 2: Forgetting degrees of freedom for t and chi-square tests — using the wrong df changes the p-value completely.
Frequently Asked Questions
What does a p-value mean in plain language?
The p-value is the probability of seeing a test statistic as extreme as yours, assuming the null hypothesis is true. A small p-value means the result would be very unlikely by chance alone, which is evidence against the null hypothesis. It is not the probability that your hypothesis is true.
When is a result statistically significant?
By convention, a p-value below 0.05 (5%) is called statistically significant, and below 0.01 is highly significant. That cutoff means a false alarm rate of 1 in 20 if the null hypothesis is true. The calculator compares your p-value with these thresholds automatically, but you should decide the significance level before collecting data.
What is the difference between one-tailed and two-tailed tests?
A two-tailed test checks for a difference in either direction — for example, whether a new teaching method changes scores at all. A one-tailed test checks a specific direction, like improvement only. For the same statistic, the two-tailed p-value is exactly double the one-tailed value, so switching tails can change a borderline conclusion.
How do I compute a p-value from a z-score?
Select the z option and enter your z-score. For a two-tailed test, the calculator computes 2 × (1 − Φ(|z|)), where Φ is the standard normal cumulative function. For example, z = 1.96 gives a two-tailed p-value of 0.05 exactly — the classic threshold used across Indian research studies and journals.
What p-value do I get for t and chi-square statistics?
For t-scores and chi-square statistics you also need the degrees of freedom. For a t-test with 10 degrees of freedom and t = 2.228, the two-tailed p-value is 0.05. For a chi-square test with 1 degree of freedom and a statistic of 3.8415, the p-value is also 0.05 — both match the printed statistical tables.
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