P-Value Calculator

Calculate a one- or two-tailed p-value from a z statistic, using the standard normal distribution.

By Konstantin Iakovlev · Updated September 2026 · Source: American Statistical Association — Statement on Statistical Significance and P-Values (2016)

p-value

0.0316

Significant (p<0.05)?

Yes

Results

Test Statistic2.1500
p-value0.031555
Significant at 0.05Yes
Significant at 0.01No

Use the P-Value Calculator above to calculate your results. Enter your values and see instant results — all calculations run in your browser.

Disclaimer: This calculator is for informational purposes only. Results are estimates based on the information you provide and the assumptions described on this page.

How It Works

A p-value answers a precise question: if the null hypothesis were true, how likely is a test statistic at least as extreme as the one your sample produced? That single number shapes decisions in fields from clinical trials to product testing. The tool returns that tail probability for the z statistic you supply.

The calculator uses the standard normal (Z) distribution for every input, computed with a polynomial approximation that agrees with the exact normal tail to within 0.000001. The one-tailed p-value is the area beyond the absolute value of your statistic, P(Z > |z|), so it assumes the tail you are testing is the one your statistic points into; the two-tailed p-value is twice that. A two-tailed z of 1.96 gives P(Z < -1.96) + P(Z > 1.96) = 0.0500. There is no t or chi-squared option and no degrees-of-freedom input, so a t statistic from a small sample gets a p-value that is too small, and the gap grows as the sample shrinks.

Your distribution choice has to match the shape and sample size of your data, because a mismatch quietly distorts the result. Note too what a p-value is not: a value below 0.05 is evidence against the null, not proof that the alternative holds, and the number says nothing about how large the underlying effect actually is.

Example: Evaluating a New Biofuel Catalyst

  1. 1 A research team tests whether a new biofuel catalyst raises yield. Over 100 trials the average yield gain is 0.25 percentage points with a standard deviation of 1.2 points. The null hypothesis is no gain; the alternative is a gain, so the test is right-tailed.
  2. 2 z = 0.25 / (1.2 / √100) = 0.25 / 0.12 = 2.083, entered as 2.08 with Test Type set to One-Tailed.
  3. 3 The calculator returns P(Z > 2.08) = 1 - 0.9812 = 0.0188.
  4. 4 Since 0.0188 < 0.05, the team rejects the null hypothesis at the 5% level; a two-tailed test would give 0.0375, still below 0.05. The p-value says nothing about whether a 0.25-point gain is worth the catalyst's cost; that is a question about effect size.

Source: American Statistical Association — Statement on Statistical Significance and P-Values (2016) · Last updated: September 2026

Frequently Asked Questions

What does a p-value actually mean?
A p-value is the probability of obtaining results at least as extreme as the observed results, assuming the null hypothesis is true. A p-value of 0.03 means that, if there were truly no effect, results at least this extreme would turn up 3% of the time. It is not the probability that the null hypothesis is true.
Is a p-value below 0.05 always significant?
The 0.05 threshold is a convention, not a universal truth. The American Statistical Association's 2016 statement on p-values warns against basing a conclusion or decision only on whether a p-value clears a cutoff. Also, a small p-value with a tiny effect size may not be practically meaningful.
What is the difference between one-tailed and two-tailed p-values?
A two-tailed test checks for an effect in either direction (greater or less), while a one-tailed test only checks one direction. Two-tailed p-values are twice the one-tailed value. Use two-tailed unless you have a strong prior reason to test only one direction.

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