basic

p-Value from z-Score Calculator

One- and two-tailed p from a standardised test statistic z.

Compute the one-tailed and two-tailed p-values from a standard-normal z-score using the Polya approximation Φ(z) ≈ ½·(1 + sign(z)·√(1 − exp(−2z²/π))). Accurate to ~0.003 over the typical hypothesis-testing range.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

Φ(z) ≈ ½·(1 + sign(z)·√(1 − e^(−2z²/π))). p_two = 1 − √(1 − e^(−2z²/π)).

In depth

Compute the one-tailed and two-tailed p-values from a standard-normal z-score using the Polya approximation Φ(z) ≈ ½·(1 + sign(z)·√(1 − exp(−2z²/π))). Accurate to ~0.003 over the typical hypothesis-testing range.