Statistics Calculators

Normal Distribution Calculator

Calculate the z-score, probability density and cumulative probability of a value within a normal (bell-curve) distribution.

Z-score —

Probability density —

P(X ≤ x) —

P(X > x) —

About the Normal Distribution Calculator

The normal distribution is the classic symmetric "bell curve" that describes many natural and statistical phenomena. This calculator converts a raw value into a z-score, finds the height of the curve at that point (density), and finds what share of the distribution lies below or above it.

Formula: z = (x − μ) ÷ σ · PDF = (1 ÷ (σ√2π)) × eᵀ⁻ᵔ²⁄²ᵝ · CDF approximated with a standard numerical formula

The cumulative probability P(X ≤ x) tells you what percentile a value falls at within a normal distribution — for example, a z-score of 0 always sits at the 50th percentile.