basic

Normal Distribution Z-Score and Percentile Calculator

z = (x − μ)/σ — standardisation and tail probability.

Calculates z-score z = (x − μ)/σ and approximate one-tailed percentile using the rational approximation of the standard normal CDF. Useful for test scores, heights, etc.

Marcus Laurent By Marcus Laurent
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

z = (x − μ) / σ; Φ(z) ≈ rational CDF approx.

In depth

Calculates z-score z = (x − μ)/σ and approximate one-tailed percentile using the rational approximation of the standard normal CDF. Useful for test scores, heights, etc.