# P-Value Calculator

Free p-value calculator. Calculate one-tailed and two-tailed p-values from z-scores or t-statistics. Determine statistical significance.

## What this calculates

Calculate the p-value from a z-score or t-statistic. Determine whether your hypothesis test result is statistically significant for one-tailed and two-tailed tests.

## Inputs

- **Test Statistic (z or t)** — Enter the z-score or t-statistic from your test.
- **Distribution Type** — options: Z (Normal), T (Student's t) — Choose z for large samples or known σ, t for small samples.
- **Degrees of Freedom (for t-distribution)** — min 1 — Degrees of freedom (n-1 for one-sample, required for t-distribution).
- **Significance Level (α)** — options: 0.01 (1%), 0.05 (5%), 0.10 (10%) — The threshold for statistical significance.

## Outputs

- **P-Value (Two-Tailed)** — P-value for a two-tailed test.
- **P-Value (Left-Tailed)** — P-value for a left-tailed test P(Z < z).
- **P-Value (Right-Tailed)** — P-value for a right-tailed test P(Z > z).
- **Significant (Two-Tailed)?** — formatted as text — Whether the two-tailed result is significant at the chosen α.
- **Significant (One-Tailed)?** — formatted as text — Whether the one-tailed result is significant at the chosen α.

## Details

The p-value is the probability of obtaining a test statistic at least as extreme as the observed value, assuming the null hypothesis is true.

Interpretation

- p < α: Reject the null hypothesis (statistically significant)

- p ≥ α: Fail to reject the null hypothesis

One-Tailed vs. Two-Tailed

- Two-tailed: tests if the value differs in either direction

- Left-tailed: tests if the value is less than hypothesized

- Right-tailed: tests if the value is greater than hypothesized

Common α levels: 0.05 (5%), 0.01 (1%), 0.10 (10%)

## Frequently Asked Questions

**Q: What does a p-value of 0.05 mean?**

A: A p-value of 0.05 means there is a 5% probability of observing a test statistic this extreme (or more extreme) if the null hypothesis is true. It does NOT mean there is a 5% chance the null hypothesis is true. At the conventional α = 0.05 level, this result is right at the border of significance.

**Q: Is a smaller p-value always better?**

A: A smaller p-value provides stronger evidence against the null hypothesis, but it does not measure the size or importance of the effect. A very small p-value can result from a large sample with a trivially small effect. Always consider effect size alongside p-values.

**Q: When should I use one-tailed vs. two-tailed test?**

A: Use a two-tailed test (default) when you want to detect differences in either direction. Use a one-tailed test only when you have a strong a priori reason to test in one specific direction AND finding a difference in the opposite direction would be treated the same as no difference. One-tailed tests are more powerful but riskier.

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Source: https://vastcalc.com/calculators/statistics/p-value
Category: Statistics
Last updated: 2026-04-21