Math

Error Function Calculator

Evaluate the error function erf(x) and its complement erfc(x).

Calculated Output

erf(x) 0.8427

erfc(x) 0.1573

Formula: erf(x) = (2/√π) ∫₀ˣ e^(−t²) dt

Step-by-Step Breakdown

1. Values used:

2. x = 1

4. erf(x) = 0.8427

5. erfc(x) = 0.1573

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The math behind it

erf(x) is the integral of a Gaussian and is computed here with the Abramowitz–Stegun rational approximation (accurate to about 7 decimal places). erfc(x) = 1 − erf(x).

Worked Example

erf(1) ≈ 0.8427, so erfc(1) ≈ 0.1573.

Frequently Asked Questions

How does this relate to the normal distribution?

The normal CDF Φ(x) = ½(1 + erf(x/√2)).

The math behind it

Worked Example

Frequently Asked Questions

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