Accueil
Calculation
Error Function
Calculate the error function erf(x) and complementary error function erfc(x).
erf(x)
-
erfc(x)
-
erf(x) = (2/√π) ∫₀ˣ e^(−t²) dt
erf(x) ≈ 1 - (a₁t + a₂t² + a₃t³ + a₄t⁴ + a₅t⁵)e^(-x²)
t = 1 / (1 + 0.3275911x)
a₁ = 0.254829592
a₂ = -0.284496736
a₃ = 1.421413741
a₄ = -1.453152027
a₅ = 1.061405429
erfc(x) = 1 - erf(x)
erf(-x) = -erf(x)
Comment utiliser
Enter x and the error function erf(x) and complementary error function erfc(x) = 1 − erf(x) are evaluated with high precision, with their defining integrals shown alongside. The error function is directly tied to the normal distribution's CDF, so this calculator stands in for statistical tables — and it also serves bit-error-rate calculations in communications and solutions of the heat equation.
- High-precision erf(x)
- Complementary erfc(x)
- Definition formulas displayed
- Handles positive and negative x
- Instant evaluation
Cas d'utilisation
- Normal-distribution probability calculations
- Bit-error-rate (BER) analysis in communications
- Evaluating heat- and diffusion-equation solutions
- Replacing statistical tables in coursework