erf

Error Function Calculator

Calculate erf(x) and erfc(x)

x value

Error Function

erf(x) = (2/√π) ∫₀ˣ e^(-t²) dt

Probability integral

Complementary

erfc(x) = 1 - erf(x)

Tail probability

Symmetry

erf(-x) = -erf(x)

Odd function

Relation to Normal

Φ(x) = (1 + erf(x/√2)) / 2

Standard normal CDF

Statistics

• Normal distribution

• Probability calculations

• Hypothesis testing

Physics

• Heat diffusion

• Particle physics

• Quantum mechanics

Engineering

• Communications theory

• Signal processing

• Reliability analysis

erf(0) = 0

erf(∞) = 1

erf(1) ≈ 0.8427

erfc(0) = 1

erfc(∞) = 0

erf(x) + erfc(x) = 1