Enter a z-score to get the two-tailed p-value — and whether the result is statistically significant at the 5% level.
What Is a P-Value Calculator?
A p-value calculator turns a z-score into significance: z = 1.96 → two-tailed p = 0.0500 — right on the 5% boundary (the unrounded p is 0.0499958, a hair below 0.05, so the tool calls it significant — a true borderline case). The p-value is the probability of seeing a result this extreme if the null hypothesis were true — not the probability the hypothesis is true. Small p: surprising under H0; large p: unsurprising.
How to Use
- Enter the z-score.
- Click “Calculate P-Value”.
Formula
Two-tailed p = 2 × (1 − Φ(|z|)).
Worked Example
z = 1.96: p = 2 × (1 − 0.9750) = 0.0500 — significant at 5%, but only just (the unrounded p is 0.0499958, a hair below 0.05).
How It Works, In Plain Words
The tool takes one number — a z-score, which says how far your result sits from what the null hypothesis expects, measured in standard deviations — and answers one question: if the null hypothesis were true, how surprising would a result this extreme be? The formula does it in three moves. First, Φ(|z|) gives the share of the normal curve below your z: for z = 1.96 that is 0.9750, as the worked example shows. Second, 1 − Φ(|z|) leaves the tail beyond it: 0.0250. Third, because the test is two-tailed — extremes count in both directions, as the FAQ puts it — the tail is doubled: p = 2 × (1 − Φ(|z|)) = 0.0500. The verdict line then compares p with 0.05: below it, significant at 5%; at or above it, not significant.
The borderline honesty is deliberate. The displayed p rounds to 0.0500, but the comparison uses the unrounded value — here 0.0499958, a hair below 0.05 — so z = 1.96 is reported significant. The sign of your z does not matter either: the formula uses |z|, the absolute value, so a result equally far in the other direction gives exactly the same two-tailed p. And the definition in the introduction bears repeating while you read the verdict: the p-value is the probability of seeing a result this extreme if the null hypothesis were true — not the probability the hypothesis is true.
Real-World Uses
A marketer finishing an A/B test — the use the benefits list names — already has a z-score from their test platform and comes here for the translation: is the observed difference surprising enough under “no real difference” to act on? The tool gives the p and the 5% verdict in one click, and the borderline example teaches them to report the actual p rather than just the word “significant”. A student checking homework by hand uses the worked example as the answer key: their calculation should land on Φ = 0.9750 and p = 0.0500 for z = 1.96, and if it does not, the formula line shows which of the three moves went wrong. A researcher screening several results uses the tool as a filter, not a judge — the trust FAQ’s caution applies: effect size, sample size and replication matter more than any single p-value they paste in.
Benefits
- P-value plus the 5% verdict
- The boundary case explained honestly
- Useful for A/B tests and research
- Pairs with the Z-Score calculator
Features of Our Tool
- Instant results in your browser
- No sign-up, no download, 100% free
- Works on mobile, tablet and desktop
- Clear step-by-step explanation below the tool
- Private — your entries never leave your device
Common Mistakes
- Reading p = 0.05 as “95% chance the effect is real” — wrong; it is about the data under H0
- Treating 0.05 as a cliff — 0.049 vs 0.051 differ negligibly
- P-hacking: testing many variants until one is “significant”
Common Mistakes to Avoid
The mistakes list covers the big three: reading p as the probability the effect is real, treating 0.05 as a cliff, and p-hacking. In prose, three more. Do not shop for a one-tailed answer when the two-tailed one disappoints: this tool is two-tailed by design — the standard default — and switching tails after seeing the data is p-hacking by another name. Do not report only the verdict: the worked example shows why the number matters, since the displayed 0.0500 hides an unrounded 0.0499958 that flips the call. And do not paste in a t-statistic or a raw difference expecting sense: the box takes a z-score only, so convert first — the related Z-Score Calculator is the usual starting point.
FAQ
What is a p-value?
The probability of data this extreme under the null hypothesis — here 0.0500.
What does p < 0.05 mean?
Conventionally “statistically significant” — unlikely enough under H0 to reject it.
Is z = 1.96 significant?
Borderline: the displayed p is 0.0500 but the unrounded value 0.0499958 sits just below 0.05, so the tool reports significant — a hair’s breadth either way.
What is a two-tailed test?
It counts extremes in both directions — the standard default.
Can I trust a single p-value?
Cautiously — effect size, sample size and replication matter more than one p-value.
Does the sign of the z-score matter?
No. The formula uses |z|, the absolute value, so z = 1.96 and z = −1.96 give the identical two-tailed p of 0.0500. That is what two-tailed means in practice: an extreme result counts whichever direction it falls, exactly as the two-tailed FAQ describes.
Why does the verdict use more decimal places than the display?
Because the display rounds to four places while the decision does not. The page’s own example is the proof: z = 1.96 displays p = 0.0500, yet the unrounded 0.0499958 sits just below 0.05, so the tool reports significant. Near the boundary, always read the worked-example logic, not just the rounded number.