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P-Value Calculator

The default z of 1.96 gives a two-tailed p of 0.0500, right at the conventional α = 0.05 threshold — which is exactly why 1.96 is the standard critical value for 95% confidence. This calculator converts a z-score to a p-value — the probability of observing a test statistic at least as extreme as yours if the null hypothesis were true; a two-tailed test uses p = 2 × (1 − Φ(|z|)), while a one-tailed test uses one tail only.

P-value
0.0500
Significant at α = 0.05
Φ(z)
0.9750
cumulative probability
Critical z (0.05)
1.960
Significant at α = 0.05
p = 0.0500 (two-tailed) falls below 0.05 — significance is about the null, not the size of the effect.
Inputs
Z-score
Test
What the p-value does and doesn't say
It's the chance of a result at least this extreme IF the null hypothesis were true — not the probability that the null is true, and not the chance you've made a mistake.
You're running a two-tailed test
Two-tailed counts both tails, so it doubles the one-tailed p. Choose one- vs two-tailed before seeing the data, based on whether you predicted a direction.
This assumes a large-sample z-test
The math treats the statistic as standard normal. For small samples a t-distribution gives more accurate tail areas than this z approximation.
Ask a follow-up
Uses your inputs above
0.0500 p-value. Want to try a variation?

The math

Reviewed 2026
Formula
two-tailed: p = 2·(1 − Φ(|z|)); one-tailed: p = 1 − Φ(|z|)
Assumes a standard normal test statistic (large-sample z-test)

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Example: how p-value is calculated

Step-by-step with default inputs

Suppose you put the default values into P-Value Calculator:

Z-score
1.96
Test
Two-tailed

Plug those into the formula two-tailed: p = 2·(1 − Φ(|z|)); one-tailed: p = 1 − Φ(|z|) and the result is:

P-value
0.0500

How does the p-value calculator work?

P-Value Calculator uses the formula shown in the math card and cites NIST/SEMATECH e-Handbook of Statistical Methods. Inputs are validated for sensible ranges; results are computed client-side for instant feedback and do not leave your browser.

References: NIST/SEMATECH e-Handbook of Statistical Methods.

Last reviewed July 2, 2026 · Editorial policy

Frequently asked questions

What does a p-value-calculator of 0.05 mean?

That there is a 5% probability of seeing a result at least this extreme purely by chance when the null hypothesis is true. It is not the probability that the null hypothesis is true — the calculation conditions on the null, not on your data.

Should I use a one-tailed or two-tailed test?

Two-tailed, unless you specified a direction before seeing the data. Two-tailed asks whether there is any difference; one-tailed asks whether it is specifically larger (or smaller). The one-tailed p is half the two-tailed p for the same z, so switching after the fact to reach significance is not legitimate.

Is z = 2 statistically significant?

Yes, at the α = 0.05 level for a two-tailed test: p ≈ 0.0455, just under the 0.05 cutoff that z = 1.96 marks exactly. For a one-tailed test the bar is lower — the critical value is z = 1.645.

What doesn't this account for?

Assumes a standard normal test statistic (large-sample z-test) For a more complete picture, combine with related calculators below.

How accurate is this p-value calculator?

The math is deterministic — the same inputs always produce the same output, and the formula is shown above. Accuracy of the answer for your situation depends on how well your inputs match reality and how well the formula models the question.

How do I share my result?

Hit Share at the top of the page. Every input you change is encoded in the URL, so a permalink reproduces exactly what you see. No account needed.