ERFCINV

The inverse complementary error function returns the real value whose complementary error function equals the provided input.

\mathrm{erfc}(\mathrm{erfcinv}(y)) = y, \quad 0 \le y \le 2

It is related to the inverse error function by \mathrm{erfcinv}(1-x)=\mathrm{erfinv}(x).

Excel Usage

=ERFCINV(y)

• y (float, required): Input value in the real domain of inverse complementary error function (dimensionless).

Returns (float): Inverse complementary error function value for the input.

Example 1: Inverse complementary error function at one

Inputs:

y
1

Excel formula:

=ERFCINV(1)

Expected output:

0

Example 2: Inverse complementary error function at one half

Inputs:

y
0.5

Excel formula:

=ERFCINV(0.5)

Expected output:

0.476936

Example 3: Inverse complementary error function at one point five

Inputs:

y
1.5

Excel formula:

=ERFCINV(1.5)

Expected output:

-0.476936

Example 4: Inverse complementary error function at one quarter

Inputs:

y
0.25

Excel formula:

=ERFCINV(0.25)

Expected output:

0.81342

Python Code

from scipy.special import erfcinv as scipy_erfcinv

def erfcinv(y):
    """
    Compute the inverse complementary error function on its real domain.

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

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

    Args:
        y (float): Input value in the real domain of inverse complementary error function (dimensionless).

    Returns:
        float: Inverse complementary error function value for the input.
    """
    try:
        y = float(y)
        return float(scipy_erfcinv(y))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

y *

Input value in the real domain of inverse complementary error function (dimensionless).