Normal Distribution Calculator

Calculate z-scores and probabilities from the normal distribution using Abramowitz & Stegun approximation.

Choose single value for P(X<x), or range to find P(a<X<b).
The value to evaluate. For range mode this is the lower bound.
The mean (average) of the distribution.
The standard deviation (must be positive).

Results

Formulas

z = (x − μ) / σ
Φ(z) uses Abramowitz & Stegun approximation (error < 1.5×10⁻⁷)
References: Normal distribution CDF via Abramowitz & Stegun (1964) approximation 26.2.17. Accuracy: |error| < 1.5×10&sup-7;. z-score: z = (x-μ)/σ.