Education
P Value Calculator
Enter a z-score and pick a tail. We compute the p-value from the standard normal distribution along with the area on each side of your z, so you can see the geometry behind the number.
Negative values are fine. ±1.96 corresponds to the 95% confidence cutoff (two-tailed). · e.g. 1.96
Tail
Two-tailed is the default for most hypothesis tests.
Two-tailed test
0.0500
from z = 1.96
A p-value is one piece of evidence. Interpret it alongside effect size, sample size, study design, and prior evidence — never as a standalone verdict.
Examples
z = 1.96, two-tailed
p ≈ 0.0500
z = 2.58, two-tailed
p ≈ 0.0099
z = 1.645, right-tailed
p ≈ 0.0500
z = −1.96, left-tailed
p ≈ 0.0250
How it works
We compute Φ(z), the cumulative area of the standard normal distribution to the left of your z-score, then derive the p-value from your chosen tail.
Two-tailed · p = 2 × (1 − Φ(|z|))
Right-tailed · p = 1 − Φ(z)
Left-tailed · p = Φ(z)
Φ(z) is computed using the Abramowitz–Stegun 7.1.26 approximation of the standard normal CDF.
A note on interpretation. A p-value is a single piece of evidence, not a verdict. Statistical significance depends on context — sample size, effect size, prior plausibility, and the quality of your study design all matter. Don 't treat any p-value threshold as automatic proof of a real effect.
Frequently asked questions
A p-value is the probability of observing a test statistic at least as extreme as yours, assuming the null hypothesis is true. A small p-value means your data would be unusual under the null — but it does not, on its own, prove the null is false.
Two-tailed tests detect a difference in either direction (the most common default). One-tailed tests are used only when you have a directional hypothesis specified before looking at the data — for example, predicting an increase but not a decrease.
There is no universal threshold. p < 0.05 is a common convention but is not a rule of nature; many fields use p < 0.01 or stricter, and the American Statistical Association has cautioned against treating any single threshold as a verdict on truth. Always interpret p-values in the context of effect size, sample size, and prior evidence.
Yes. We use the Abramowitz–Stegun approximation of the standard normal CDF (mean 0, standard deviation 1). For tests on other distributions (t, χ², F), the conversion is different — this calculator is for z-scores only.
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