Half-Normal Distribution Calculator

About this calculator

The half-normal distribution is what you get by folding a normal distribution centered at zero over onto its positive side — equivalently, it’s the distribution of |Z| when Z follows a normal distribution N(0, σ²). It has a single scale parameter σ, probability density function f(x) = √(2/π)/σ · exp(−x²/2σ²) for x ≥ 0, and mean σ√(2/π) — always positive by construction, unlike the parent normal distribution.

This calculator evaluates the PDF, cumulative probability (CDF), and mean of the half-normal distribution for a chosen x and σ. It shows up wherever a quantity is naturally non-negative but arises from folding or taking the absolute value of an underlying normal process: modeling measurement or manufacturing error magnitudes (where only the size of a deviation matters, not its sign), reliability and survival analysis, and as a common prior distribution for standard-deviation parameters in Bayesian statistics because it’s supported only on positive values.