P-Value Calculator (z to p)

Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.

Inputs

Result

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General calculation reads

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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.

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