If you already have a z-score and need the corresponding p-value, this calculator gives it instantly. It supports left-tailed, right-tailed, and two-tailed tests, so you can use it for common z-tests in statistics, hypothesis testing, quality control, and research reporting.
Z-Score to P-Value Calculator
Enter your z-score and select the test direction.
Tip: Press Enter inside the z-score field to calculate quickly.
What is a p-value from a z-score?
A p-value tells you how extreme your test statistic is under the null hypothesis. When your test statistic is a z-score, you can convert it to probability using the standard normal distribution. In plain terms: it answers, “If the null were true, how likely is a value this extreme (or more extreme)?”
This is often called a z to p-value conversion, and it is one of the most common steps in introductory and applied statistics.
How the calculator works
Step 1: Compute the cumulative probability Φ(z)
The symbol Φ(z) is the standard normal cumulative distribution function (CDF). It returns the area to the left of z under a standard normal curve.
Step 2: Apply your test type
- Left-tailed test: p = Φ(z)
- Right-tailed test: p = 1 − Φ(z)
- Two-tailed test: p = 2 × min(Φ(z), 1 − Φ(z))
The two-tailed formula doubles the smaller tail area and is capped at 1. This is the standard approach when the alternative hypothesis is “not equal to.”
Examples
Example 1: z = 1.96 (two-tailed)
Φ(1.96) is about 0.9750. The right tail is about 0.0250. Two-tailed p-value is 2 × 0.0250 = 0.0500. At α = 0.05, this lands right at the common threshold.
Example 2: z = 2.33 (right-tailed)
Right-tail p-value is approximately 1 − Φ(2.33) ≈ 0.0099. This is less than 0.01, so evidence against the null is strong for a one-sided test in the right direction.
Example 3: z = -1.50 (left-tailed)
Left-tail p-value is Φ(-1.50) ≈ 0.0668. At α = 0.05, this is not statistically significant.
Common mistakes to avoid
- Using the wrong tail: Match the p-value type to your alternative hypothesis before calculating.
- Forgetting to double in two-tailed tests: A frequent source of incorrect conclusions.
- Interpreting p as the probability the null is true: It is not. It is a probability conditioned on the null being true.
- Ignoring effect size: A small p-value does not automatically imply practical importance.
When this z-score p-value calculator is appropriate
Use this tool when your test statistic is approximately normal or exactly normal under the null—common for large-sample proportion tests, mean tests with known variance, and many standardized score settings. If your method requires a t, chi-square, or F distribution, use the matching calculator instead of this one.
Quick interpretation guide
- p < α: Reject the null hypothesis (statistically significant).
- p ≥ α: Fail to reject the null hypothesis (not statistically significant).
Always report context, assumptions, confidence intervals, and effect size alongside p-values for stronger scientific communication.
FAQ
Can I use negative z-scores?
Yes. Negative z-scores are valid and often expected. The tail selection determines how that z-score maps to the final p-value.
What if my p-value is extremely small?
The calculator automatically displays tiny probabilities in scientific notation when needed.
Is this equivalent to z-table lookup?
Yes. It performs the same conversion as a z-table, but with direct support for left, right, and two-tailed outputs.