ERFC

The complementary error function gives the remaining Gaussian integral tail beyond the origin-shifted error function, and satisfies \mathrm{erfc}(x)=1-\mathrm{erf}(x).

\mathrm{erfc}(x)=\frac{2}{\sqrt{\pi}}\int_x^{\infty} e^{-t^2}\,dt

This wrapper evaluates \mathrm{erfc}(x) for a scalar real argument using SciPy.

Excel Usage

=ERFC(x)

• x (float, required): Real argument for the complementary error function (dimensionless).

Returns (float): Complementary error function value at the input.

Example 1: Complementary error function at zero

Inputs:

x
0

Excel formula:

=ERFC(0)

Expected output:

1

Example 2: Complementary error function at one

Inputs:

x
1

Excel formula:

=ERFC(1)

Expected output:

0.157299

Example 3: Complementary error function at negative half

Inputs:

x
-0.5

Excel formula:

=ERFC(-0.5)

Expected output:

1.5205

Example 4: Complementary error function at two

Inputs:

x
2

Excel formula:

=ERFC(2)

Expected output:

0.00467773

Python Code

from scipy.special import erfc as scipy_erfc

def erfc(x):
    """
    Evaluate the complementary error function for a real input.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.erfc.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        x (float): Real argument for the complementary error function (dimensionless).

    Returns:
        float: Complementary error function value at the input.
    """
    try:
        x = float(x)
        return float(scipy_erfc(x))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

x *

Real argument for the complementary error function (dimensionless).