P-value Calculator

Written byOleh Soloninupdated 10 September 2026

z value

Test type

Significance level α

Result

p-value0.049996
p as a percentage5%
Critical z1.96
VerdictThe null hypothesis is rejected
Confidence level, %95%
Testtwo-tailed

The chance of seeing this by luck alone

The p-value for a one-tailed or two-tailed test, the critical z value, and a plain verdict at your significance level.

A p-value is the probability of a result at least this extreme if the null hypothesis is true. A small p means chance is a poor explanation of the data, so the hypothesis is rejected.

The 0.05 threshold is a convention traceable to Fisher, not a law of nature. The gap between p = 0.049 and p = 0.051 is negligible, and treating them as categorically different is a familiar methodological mistake.

What this calculator shows

The p-value as a fraction and as a percentage
The critical z value for your significance level
A verdict on whether the null hypothesis is rejected

What to keep in mind

The normal distribution is used; small samples call for the t-distribution, which gives a slightly larger p.
A two-tailed test doubles the one-tailed value, appropriate when a deviation in either direction matters.

FAQs

What does a p-value actually mean?

The probability of data this extreme or more, assuming the null hypothesis holds. It is not the probability that the hypothesis is true — a widespread and consequential misreading.

Why is the threshold 0.05?

Fisher proposed it as a convenient benchmark. Particle physics demands five sigma, roughly p = 0.0000003 — the threshold should follow the cost of being wrong.

When is a one-tailed test appropriate?

When a deviation the other way is meaningless or ruled out in advance. Choosing one-tailed after seeing the data is not legitimate.

What if p is just above 0.05?

Do not declare no effect. Absence of statistical significance is not evidence of absence — often it just means the sample was small.

Worked example

The textbook boundary

Input: z = 1.96, two-tailed, α = 0.05

Output: p = 0.05, critical z = 1.96

Note: 1.96 is the value that gives exactly five percent two-tailed — the same number behind every 95 percent confidence interval.

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P-value Calculator

Result

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