Admittance Calculator

The Admittance Calculator converts the rectangular form of complex admittance into a magnitude in siemens (S) and a phase angle in degrees.

In AC analysis, admittance is the reciprocal of impedance and describes how readily a circuit path accepts current at a stated voltage and frequency. It is commonly written as:

(Y = G + jB)

Where:

• Y = complex admittance, in siemens
• G = conductance, the real component, in siemens
• B = susceptance, the imaginary component, in siemens
• j = imaginary operator

The calculator returns the polar form:

(Y = |Y| angle theta)

This form is useful when comparing AC branches, combining parallel circuit paths, evaluating capacitive or inductive effects, and converting between voltage-current phasor relationships.

Conductance and Susceptance

Enter Conductance as the real part of admittance. The separate Conductance Calculator covers the reciprocal resistance relationship; the worksheet uses conductance as one component of a complex AC quantity.

Enter Susceptance as the imaginary part of admittance. Susceptance represents the reactive portion of admittance:

• Positive susceptance is associated with a capacitive characteristic.
• Negative susceptance is associated with an inductive characteristic.

Both entries use siemens, abbreviated S. One siemens is equivalent to one ampere per volt:

\(\displaystyle 1\text{ S} = 1\text{ A/V}\)

For a purely resistive branch, susceptance is zero. A nonzero susceptance shows the reactive part of the admittance; for example, 0.1 S conductance and 0.05 S susceptance produce:

\(\displaystyle Y = 0.1 + j0.05\text{ S}\)

Its magnitude is approximately 0.1118 S, and its phase angle is approximately 26.565 degrees.

Calculation Formula

The calculator uses standard complex-admittance arithmetic.

Admittance magnitude

\(\displaystyle |Y| = \sqrt{G^2 + B^2}\)

Where:

• |Y| = Admittance magnitude
• G = Conductance
• B = Susceptance

Admittance phase

\(\displaystyle \theta = \operatorname{atan2}(B,G)\)

The phase calculation uses the signs of both conductance and susceptance so the result is placed in the proper quadrant. The displayed Admittance phase is expressed in degrees.

A positive phase indicates a positive imaginary component. A negative phase indicates a negative imaginary component.

Calculation Example

Using the calculator’s example inputs:

Field	Value
Conductance	0.1 S
Susceptance	0.05 S

The complex admittance is:

\(\displaystyle Y = 0.1 + j0.05\text{ S}\)

Magnitude:

\(\displaystyle |Y| = \sqrt{(0.1)^2 + (0.05)^2} \approx 0.1118\text{ S}\)

Phase:

\(\displaystyle \theta = \operatorname{atan2}(0.05,0.1) \approx 26.565^\circ\)

Result:

Output	Result
Admittance magnitude	0.1118 S
Admittance phase	26.565 deg

The result describes an admittance with both conductive and capacitive components under the stated sign convention.

Using Admittance in AC Circuit Work

Admittance is especially convenient for parallel AC circuits because individual branch admittances add directly:

\(Y_T = Y_1 + Y_2 + Y_3 + cdots\)

After determining total admittance, circuit current can be found from:

(I = VY)

For a phasor voltage and complex admittance, the current magnitude is:

\(\displaystyle |I| = |V| \times |Y|\)

The current phase relationship is determined by the voltage phase plus the Admittance phase.

In practical engineering and troubleshooting work, admittance calculations can support evaluation of parallel loads, power-factor-correction capacitor banks, filter networks, transformer equivalent circuits, and feeder or branch-circuit load models. The calculated value may also be converted back to impedance when impedance is needed for a separate analysis:

\(\displaystyle Z = \frac{1}{Y}\)

Installation and Code Limits

The calculation performs ideal complex-admittance arithmetic from Conductance and Susceptance. It does not select capacitors, inductors, conductors, overcurrent protection, raceways, or other installation components.

The result does not establish branch-circuit or feeder ampacity, conductor AWG or kcmil size, terminal rating, insulation temperature rating, adjustment factor, correction factor, voltage-drop compliance, available fault current, or equipment suitability. Those decisions require the actual system voltage, frequency, load characteristics, conductor and terminal information, equipment listings, applicable NEC requirements, and AHJ requirements.

For field use, confirm that conductance and susceptance values are based on the correct operating frequency and circuit condition. Harmonics, nonlinear loads, switching equipment, capacitor tolerances, transformer characteristics, and changing load conditions can make a simplified admittance value unsuitable for installation approval or final equipment selection.