π Statistics & Probability
P Value Calculator
Calculate p-value from a z-score or t-score. Free p-value calculator for one-tailed and two-tailed tests.
What This Calculator Tells You
This calculator converts a z-score into a p-value: the probability of seeing a result at least that extreme if there were really no effect. It also tells you whether the result clears the common 0.05 significance threshold.
Use it when you already have a z-statistic β from an A/B test, a survey comparison or a textbook problem β and need the matching p-value.
What to Enter
- Z-score β your test statistic. Positive or negative; the calculator uses its size.
- Tails (1 or 2) β use 2 (the default) when a difference in either direction matters, which is the usual case. Use 1 only if you decided in advance that you only care about one direction.
Worked Examples
1. The famous 1.96
z = 1.96, two-tailed.
- Result β p = 0.0500 β exactly at the conventional threshold. This is why 1.96 is the critical value for 95% confidence.
2. A significant A/B test
An A/B test with 10,000 visitors per variant and conversion rates of 4.0% vs 4.8% produced z = 2.758.
- Result β p = 0.0058 β significant. Matches the result from the A/B test calculator.
3. One-tailed vs two-tailed
- z = 1.645, one-tailed β p = 0.0500.
- z = 1.5, two-tailed β p = 0.1336 β not significant. The same z-score gives half that p-value one-tailed (about 0.067), which is why choosing tails after seeing the data is a form of cheating.
How It’s Calculated
- z: Z-score (standard normal)
- p: Sample proportion / p-value
How to Read Your Result
- p < 0.05: conventionally "statistically significant" β a result this extreme would happen less than 5% of the time with no real effect.
- p β₯ 0.05: not enough evidence to rule out chance. Not proof that there is no effect.
- The p-value is not the probability your hypothesis is true. It assumes no effect and asks how surprising the data is.
- Report the effect size too. A tiny p-value with a trivial difference is rarely worth acting on.
Common Mistakes to Avoid
- Switching to one-tailed after the fact to push a result under 0.05.
- Treating 0.049 and 0.051 as opposites. They represent almost identical evidence.
- Running many tests and reporting the significant one. With 20 comparisons, one will likely hit p < 0.05 by chance alone.
- Using a z-test for small samples where a t-test is appropriate.
When to Use This Calculator
- Convert a z-statistic from a report or paper into a p-value.
- Double-check A/B test results.
- Work through statistics homework.
- Find the significance of a survey comparison.
Frequently Asked Questions
What is a p-value in simple terms?
The chance of getting a result at least as extreme as yours if nothing were really going on. Small p-values suggest something real is happening.
Should I use one or two tails?
Two, unless you committed before collecting data to caring about only one direction. Two-tailed is the safer default.
Why 0.05?
It is a convention, not a law. Some fields use 0.01 or stricter; low-risk business decisions sometimes accept 0.10. Choose the threshold before you look at results.
How is this related to the z-score calculator?
The z-score calculator standardizes a single value. This calculator takes a z-statistic from a test and converts it into a p-value. Read z-scores and p-values explained.
Do you store the values I enter?
No. All calculations happen in your browser. Your data never leaves your device.
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