All three tail options
Two-tailed, left-tailed, and right-tailed from the same z, so you do not have to halve numbers by hand.
Tools / P Value Calculator
P Value Calculator
Enter a z-score, pick one or two tails, and get the p-value with a plain reading of whether it clears the usual 0.05 threshold.
Two-tailed: p = 2 × (1 − Φ(|z|))
Enter values to see the result
- 1
Enter the z-score
From a z-test, a proportion test, or the z score calculator on this site.
- 2
Choose the tails
Two-tailed is the default and the right choice unless your hypothesis was directional before you saw the data.
- 3
Read the p-value
Below 0.05 is conventionally called significant. The result also shows the value against the common thresholds.
Why this p-value calculator
Reading a p-value off a printed z-table is slow and easy to get wrong at the tails. This does the same lookup exactly.
Accurate in the tails
Uses a numerical normal CDF rather than a rounded table, so very small p-values stay usable.
Threshold context
The result is compared against 0.05, 0.01, and 0.001 so you can see where it lands.
When you need a p-value
A/B test readouts
Turn the z-statistic from a proportion test into a p-value for the write-up.
Coursework and exams
Check a z-table lookup without squinting at four decimal places.
Research reporting
Report an exact p-value rather than the vague p < 0.05.
How the p-value is derived
Two-tailed: p = 2 × (1 − Φ(|z|)) · Right: p = 1 − Φ(z) · Left: p = Φ(z)
Φ is the standard normal cumulative distribution function, the area to the left of z. A two-tailed test counts extreme results in both directions, which is why it doubles the one-tailed area.
What a p-value does and does not tell you
- It is the probability of data at least this extreme if the null hypothesis were true.
- It is not the probability that the null hypothesis is true.
- A small p-value with a tiny effect size is often not worth acting on.
- Running many comparisons inflates the chance of a false positive, so adjust the threshold when you do.
Related calculators
Frequently asked questions
How do you calculate a p-value from a z-score?
For a two-tailed test, take the area beyond the absolute z in both tails:
p = 2 × (1 − Φ(|z|))
A z of 1.96 gives p ≈ 0.05, and a z of 2.58 gives p ≈ 0.01. One-tailed tests use a single tail, so the p-value is half as large.
What does a p-value of 0.05 mean?
If the null hypothesis were true, there would be a 5% chance of seeing a result at least this extreme by chance alone.
It is a convention, not a law of nature. Some fields use 0.01, and some pre-register a different threshold entirely.
Should I use one or two tails?
Two-tailed unless you committed to a direction before collecting data. Two-tailed asks whether there is any difference; one-tailed asks whether there is a difference in one specific direction.
Switching to one-tailed after seeing the result doubles your effective false positive rate, which is why reviewers push back on it.
What does a non-significant p-value mean?
That you did not find enough evidence against the null hypothesis, not that the null is true. A small sample can hide a real effect easily.
Check whether your sample size was adequate before concluding there is no difference.
Can a p-value be zero?
Not exactly. Very large z-scores produce p-values so small they round to zero in floating point, which is conventionally reported as p < 0.001 rather than p = 0.
How do I get a p-value for an A/B test?
Use the statistical significance calculator. Enter visitors and conversions for each variant and it runs the two-proportion z-test and returns the p-value directly.
Are my numbers stored?
No. The calculation happens in your browser.
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