In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of impedance. The SI unit of admittance is the siemens (symbol S). Oliver Heaviside coined the term admittance in December 1887.[1]

$Y \equiv \frac{1}{Z} \,$

where

Y is the admittance, measured in siemens
Z is the impedance, measured in ohms

The synonymous unit mho, and the symbol ℧ (an upside-down uppercase omega Ω), are also in common use.

Resistance is a measure of the opposition of a circuit to the flow of a steady current, while impedance takes into account not only the resistance but also dynamic effects (known as reactance). Likewise, admittance is not only a measure of the ease with which a steady current can flow, but also the dynamic effects of the material's susceptance to polarization:

$Y = G + j B \,$

where

• $Y$ is the admittance, measured in siemens.
• $G$ is the conductance, measured in siemens.
• $B$ is the susceptance, measured in siemens.
• $j^2 = -1$

## Conversion from impedance to admittance

Parts of this article or section rely on the reader's knowledge of the complex impedance representation of capacitors and inductors and on knowledge of the frequency domain representation of signals.

The impedance, Z, is composed of real and imaginary parts,

$Z = R + jX \,$

where

• R is the resistance, measured in ohms
• X is the reactance, measured in ohms
$Y = Z^{-1}= \frac{1}{R + jX} = \left( \frac{1}{R^2 + X^2} \right) \left(R - jX\right)$

Admittance, just like impedance, is a complex number, made up of a real part (the conductance, G), and an imaginary part (the susceptance, B), thus:

$Y = G + jB \,\!$

where G (conductance) and B (susceptance) are given by:

\begin{align} G &= \Re(Y) = \frac{R}{R^2 + X^2} \\ B &= \Im(Y) = -\frac{X}{R^2 + X^2} \end{align}

The magnitude and phase of the admittance are given by:

\begin{align} \left | Y \right | &= \sqrt{G^2 + B^2} = \frac{1}{\sqrt{R^2 + X^2}} \\ \angle Y &= \arctan \left( \frac{B}{G} \right) = \arctan \left( -\frac{X}{R} \right) \end{align}

where

• G is the conductance, measured in siemens
• B is the susceptance, also measured in siemens

Note that (as shown above) the signs of reactances become reversed in the admittance domain; i.e. capacitive susceptance is positive and inductive susceptance is negative.