About this P-Value Calculator
The P-value is a probability score used in hypothesis testing to determine the significance of results. It tells you the probability of obtaining test results at least as extreme as the results actually observed, assuming the null hypothesis is correct.
Who this calculator is for
- Students and researchers interpreting the result of a z-test or normal-approximation hypothesis test.
- Analysts who already have a z-score and need the corresponding tail probability.
- Anyone deciding whether a result crosses a chosen significance threshold such as 0.05.
When to use it
- Use it after calculating a z-score for a one-tailed or two-tailed hypothesis test.
- Use it to compare the same test statistic against different significance cutoffs.
- Use it when you want a quick significance check before reporting results.
How to use this calculator
- Enter the Z-score (test statistic).
- Select the Test Type (One-Tailed or Two-Tailed).
- For One-Tailed, interpret the sign of the Z-score as the direction of the tail: positive Z uses the right tail and negative Z uses the left tail.
- The tool calculates the P-value.
Key assumptions
- This calculator expects a z-score from a z-test or normal-approximation workflow.
- Choose one-tailed only when your hypothesis was directional before you saw the data.
- The p-value is evidence against the null hypothesis, not the probability that the null or alternative is true.
Accuracy and testing
Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.
How this calculator works
Inputs explained
Z-Score
The number of standard deviations a data point is from the mean. Calculated using a Z-test formula.
Test Type
Two-tailed tests check for any difference (higher or lower). One-tailed tests check for a specific direction, using the sign of the Z-score to choose the left or right tail.
Understanding your results
Example scenarios
Significant Result
Z = 2.5. Two-Tailed P = 0.0124. Since 0.0124 < 0.05, the result is statistically significant.
Not Significant
Z = 1.0. Two-Tailed P = 0.3173. Since 0.3173 > 0.05, the result is not significant.
Key Features
- One-Tailed & Two-Tailed Logic
- High Precision Probability
- Z-Test Support
Tips & Best Practices
- The standard threshold for significance (alpha) is 0.05, but some fields require 0.01 or even lower.
- Two-tailed tests are more conservative and are the standard choice unless you have a specific reason to look in only one direction.
Glossary of Terms
- Null Hypothesis (H0)
- The default assumption that there is no relationship between two measured phenomena.
- Significance Level (α)
- The probability of rejecting the null hypothesis when it is true (Type I error). Usually set at 0.05.