Error Function Calculator

Compute erf(x), erfc(x), erfi(x), and the scaled error function. Used in statistics, probability, and heat transfer.

Calculate Error Function

erf(x)
(2/√π)∫₀ˣ e⁻ᵗ² dt
erfc(x)
1 − erf(x)
erf(−x)
Odd function: −erf(x)
erfcx(x)
eˣ² · erfc(x)
Key properties: erf(0) = 0 · erf(∞) = 1 · erf is odd: erf(−x) = −erf(x) · erf(x) + erfc(x) = 1
Statistics link: Φ(x) = ½[1 + erf(x/√2)] where Φ is the standard normal CDF
Relation at x=1: erf(1) ≈ 0.8427 (about 84.27% probability within 1σ for normal distribution)

erf(x) Table

xerf(x)erfc(x)