P-Value Calculator
Calculate the one-tailed and two-tailed p-value corresponding to a z-score from the standard normal distribution.
Significant
A two-tailed p-value of 5% falls below the common 5% significance threshold — usually read as a statistically significant result.
- Two-Tailed P-Value0.05
About the P-Value Calculator
A p-value measures how surprising an observed result would be if there were actually no real effect going on — in statistics terms, if the 'null hypothesis' were true. A small p-value means the result would be unusual under that assumption, which is the standard evidence researchers lean on to say an effect is probably real rather than just noise.
This is the calculator behind hypothesis testing in research papers, A/B test analysis, and any statistics coursework that gets to the 'is this result actually significant' stage — taking a z-score (how many standard deviations a result sits from what you'd expect by chance) and converting it into the probability researchers actually report.
The distinction between one-tailed and two-tailed matters here: a one-tailed p-value only asks about surprise in one direction (result higher than expected, say), while a two-tailed p-value accounts for surprise in either direction — and two-tailed is the more common, more conservative default in most published research.
How it’s calculated
This works from the standard normal distribution: the one-tailed p-value is 1 minus the cumulative probability up to |z|, which is the probability of seeing a result at least that extreme in one specific direction purely by chance.
The two-tailed p-value simply doubles that figure, since it accounts for an extreme result showing up in either direction — above or below the expected value — rather than just the one direction the one-tailed version checks.
A larger z-score (further from zero) pushes the p-value down, since it represents a result that's further out in the distribution's tail and therefore less likely to happen just by chance if there were no real effect at all.
Frequently asked questions
What counts as a statistically significant p-value?
The most common threshold is 0.05 (5%) — a p-value below that is conventionally called statistically significant. Some fields use stricter thresholds like 0.01, particularly when false positives carry a higher cost.
Should I use a one-tailed or two-tailed p-value?
Use two-tailed by default — it's the more conservative, more widely accepted choice and covers surprise in either direction. One-tailed is only appropriate when you have a specific, pre-stated reason to only care about one direction of effect before you look at the data.
Does a p-value tell you the probability the null hypothesis is true?
No — that's one of the most common misreadings of it. A p-value only measures how surprising the observed data would be if the null hypothesis were true, not the probability that the null hypothesis itself is true or false.
What's the relationship between a z-score and a p-value?
The z-score measures how many standard deviations a result is from what's expected by chance; the p-value converts that distance into a probability. A larger z-score (further from zero, in either direction) always produces a smaller, more significant p-value.
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