P-Value Calculator (z to p)
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.
Result
Loading calculator…
—
How to use this calculator
- Compute z-score from your data.
- Pick tail type.
- Read p and significance.
About this calculator
A p-value is the probability of seeing test results at least as extreme as observed, assuming the null hypothesis is true. Smaller p ⇒ stronger evidence against H₀. Conventional threshold: p < 0.05 for "significant"; p < 0.01 for "highly significant". Two-tailed test (|z|) is appropriate when alternative is two-sided; one-tailed when direction is pre-specified. Calculator uses Abramowitz-Stegun normal CDF approximation (~7 decimal accuracy).
Frequently asked
Why 0.05?+
Convention from Fisher (1925). Loosely: 1-in-20 false positive rate is acceptable for many fields. Increasingly criticized in favor of pre-registration and effect-size emphasis.
Two-tailed vs. one-tailed?+
Two-tailed: alternative H₁ is "different from null" (most common). One-tailed: H₁ is directionally specified before seeing data. One-tailed gives smaller p but only if pre-specified.
P doesn't prove anything?+
Correct. P-value is conditional probability of data given null. Not the probability the null is true. Bayesian methods address this directly.
Multiple comparisons?+
Running 20 tests at α = 0.05: ~1 false positive expected. Use Bonferroni (α/n) or False Discovery Rate adjustments.
Effect size matters too?+
Yes — a tiny effect can be "significant" with huge n. Always report effect size + CI alongside p.
Related calculators
Normal Distribution Calculator (PDF + CDF)
Compute probability density and cumulative probability at x for given μ, σ.
Confidence Interval Calculator
CI = mean ± z × (σ/√n). 90 / 95 / 99 % standard intervals.
Binomial Probability Calculator
P(X = k) = C(n,k) p^k (1−p)^(n−k). Probability of exactly k successes in n trials.
Combinations Calculator C(n, r)
C(n, r) = n! / (r!(n−r)!). Number of ways to choose r items from n where order doesn't matter.
Permutations Calculator P(n, r)
P(n, r) = n! / (n−r)!. Number of ways to arrange r items from n where order matters.
Pearson Correlation Coefficient
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].