basic

Z-Score to Percentile Calculator

Cumulative normal probability Φ(z).

Convert a standard-normal z-score into the corresponding cumulative percentile (Φ(z)) using a high-accuracy logistic approximation. Reports the lower-tail percentile and the two-tail p-value.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

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 + tanh(0.797885·z·(1 + 0.044715·z²))). Two-tail p = 2·(1 − Φ(|z|)).

In depth

Convert a standard-normal z-score into the corresponding cumulative percentile (Φ(z)) using a high-accuracy logistic approximation. Reports the lower-tail percentile and the two-tail p-value.