P-Value Calculator

Q: How do you find a p-value from a z-score?

Two-tailed: p = 2 × (1 − Φ(|z|)), where Φ is the standard normal CDF. For z = 1.96, Φ = 0.975, so p = 2 × 0.025 = 0.05. One-tailed, drop the factor 2.

Q: When is a result statistically significant?

When the p-value is less than or equal to the significance level α chosen in advance, usually 0.05. p = 0.03 is significant at α = 0.05 but not at α = 0.01.

Q: How do I get the p-value for a t-test?

Compute the t statistic and its degrees of freedom (one sample: df = n − 1), then take the area of the t distribution beyond t. The calculator does both straight from x̄, s and n.

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

If the null hypothesis were true, a result this extreme or more would occur in about 5% of repeated studies. It is not a 95% chance that the effect is real.

Q: How do I find the p-value for a chi-square test?

It is the area to the right of your χ² value. With 1 degree of freedom the 5% cut-off is χ² = 3.841, so larger values are significant at α = 0.05.

This p-value calculator works from any test statistic: choose z, t or chi-square, enter the value and pick one- or two-tailed. For t-tests, the means, standard deviations and sample sizes are enough.

Example: What do you have: z-score (normal distribution) · Alternative hypothesis: two-tailed (≠) · Significance level α 0.05 · z-score 1.96 → P-value: p = 0.04999579. Source: 1.3.6.6.1, NIST/SEMATECH e-Handbook – Normal distribution. Updated: 30 September 2026.

What do you have?

Alternative hypothesis

Significance level α

commonly 0.05 (5%) or 0.01

z-score

My ToolboxYour inputs are saved in this browser only.

Result

P-value: p = 0.04999579
Decision: Significant: p = 0.04999579 ≤ α = 0.05 – reject the null hypothesis.
Test statistic: z = 1.96
Critical value: ±1.95996
Confidence interval: –
Working: p = 2 · P(z > |1.96|) = 0.04999579
Compare: 0.04999579 ≤ 0.05 → reject H₀; The p-value is the probability of a result at least this extreme if the null hypothesis were true – not the probability that the null hypothesis is true.

How it is calculated

A p-value is the probability of getting a test result at least as extreme as yours if the null hypothesis is true. If it is at or below the significance level α (usually 0.05), the result is called statistically significant. Examples: z = 1.96 two-tailed gives p ≈ 0.050; t = 2.0 with 35 degrees of freedom gives p ≈ 0.053.

How the p-value is calculated

From a z-score: the area under the standard normal curve beyond z; two-tailed it is doubled: p = 2 × (1 − Φ(|z|)).
From a t-score: the same with the t distribution and df degrees of freedom – with small samples its tails are heavier than the normal curve.
From chi-square: the area to the right of χ² with df degrees of freedom (goodness-of-fit and independence tests).
t-test from summary statistics: one-sample t = (x̄ − μ₀) ÷ (s ÷ √n); Welch’s test for two groups with unequal variances and Welch–Satterthwaite degrees of freedom.

One-tailed or two-tailed?

Use a two-tailed test when any difference matters (H₁: μ ≠ μ₀). Use a one-tailed test only if the direction was fixed before collecting the data (H₁: μ > μ₀ or μ < μ₀). A one-tailed p-value in the predicted direction is half the two-tailed one – picking the direction afterwards inflates false positives.

What a p-value does not tell you

As the American Statistical Association stresses, a p-value does not measure the probability that a hypothesis is true, nor the size or importance of an effect. Report an effect size and a confidence interval as well – the calculator gives the interval for the mean difference in t-tests.

Accuracy

The distributions are computed with the incomplete gamma and beta functions (NIST DLMF) and match the NIST/SEMATECH e-Handbook tables – to about 12 digits instead of the 3–4 digits of printed tables. Get the mean and standard deviation from raw data with the standard deviation calculator, work with rates in the percentage calculator, or evaluate formulas in the scientific calculator.

Frequently asked questions

How do you find a p-value from a z-score?

Two-tailed: p = 2 × (1 − Φ(|z|)), where Φ is the standard normal CDF. For z = 1.96, Φ = 0.975, so p = 2 × 0.025 = 0.05. One-tailed, drop the factor 2.

When is a result statistically significant?

When the p-value is less than or equal to the significance level α chosen in advance, usually 0.05. p = 0.03 is significant at α = 0.05 but not at α = 0.01.

How do I get the p-value for a t-test?

Compute the t statistic and its degrees of freedom (one sample: df = n − 1), then take the area of the t distribution beyond t. The calculator does both straight from x̄, s and n.

What does a p-value of 0.05 mean?