Normal Distribution Calculator

Find the z-score, cumulative probability, area between two values and the value at a given percentile of a normal distribution, free online.

Mean (μ)

Standard deviation (σ)

Value x

Second value x₂ (for an area between) (optional)

Percentile (0–100) to find x (optional)

About this calculator

For X ~ N(μ, σ²): z = (x − μ) ÷ σ, P(X < x) = Φ(z). Enter a second value to get P(x₁ < X < x₂), or a percentile to find the x that leaves that fraction of the distribution below it.