How this calculator works
The error function is a scaled integral of exp(-t^2). Its complement erfc is evaluated directly in the positive tail to avoid subtracting a value very close to one. The inverses use monotone bisection in the tails and direct Newton iteration for inverse erf near zero. Tail comparison uses logarithms to support very small positive inputs. All arguments are dimensionless, and infinite inverse endpoints are rejected. A significant-digit text readout preserves tiny values that the fixed-decimal numeric readout may show as zero. Calculations remain limited by floating-point precision.
Formula
erf(x) = 2/sqrt(pi) integral from 0 to x of exp(-t^2) dt. erfc(x) = 1 - erf(x). erf^(-1)(y) = erfc^(-1)(1-y).
Worked example
erf(1) is approximately 0.84270079295, so erfc(1) is approximately 0.15729920705. Since erfc(0) = 1, inverse erfc(1) = 0.
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Frequently asked questions
Can I enter y = 1 for inverse erf?
No. The inverse approaches positive infinity at 1 and negative infinity at -1.
Why use erfc for small tails?
A direct complementary calculation preserves small positive tails that would be lost by subtracting a rounded erf value from one.
Is erf a probability?
Not for every input: erf is negative for negative inputs. It connects to the standard normal CDF through Phi(z) = (1 + erf(z/sqrt(2)))/2.