# RLC Admittance Calculator (Y = G + jB)

Compute complex admittance Y = 1/Z = G + jB for series or parallel RLC circuits: G = R/|Z|², B = −X/|Z|². Returns conductance, susceptance, magnitude and phase angle. Supports any subset of R/L/C.

> Canonical page: https://elysiatools.com/en/tools/admittance-calculator

- **Category:** Math & Numbers

- **Keywords:** admittance, conductance, susceptance, Y = 1/Z, G + jB, RLC, AC circuits, siemens, electrical engineering

## Overview

The RLC Admittance Calculator computes the complex admittance (Y = G + jB) for series or parallel AC circuits containing any combination of resistors, inductors, and capacitors. By inputting the circuit topology, component values, and operating frequency, you can instantly determine the conductance (G), susceptance (B), admittance magnitude, and phase angle to analyze AC circuit behavior.

## Inputs

- **Topology** (select)
- **Resistance R (Ω)** (number): Optional. At least one of R/L/C must be provided.
- **Inductance L (H)** (number): Optional. At least one of R/L/C must be provided.
- **Capacitance C (F)** (number): Optional. At least one of R/L/C must be provided.
- **Frequency f (Hz)** (number): e.g. 50
- **Decimal Places** (number)

## When to use

- When analyzing parallel AC circuits where adding admittances is mathematically simpler than combining complex impedances.
- When designing impedance matching networks, filters, or resonant circuits and you need to determine the conductance and susceptance at a specific frequency.
- When converting series RLC impedance values into their equivalent parallel admittance representations for power system or RF analysis.

## How it works

- Select the circuit topology (series or parallel) and enter the operating frequency in Hertz.
- Input the values for resistance (R), inductance (L), and/or capacitance (C) as required for your circuit configuration.
- The calculator computes the inductive reactance (X_L = 2πfL) and capacitive reactance (X_C = 1 / (2πfC)) to find the total impedance (Z).
- It calculates the complex admittance (Y = 1/Z = G + jB), outputting the conductance (G), susceptance (B), magnitude (|Y|), and phase angle.

## Use cases

- Calculating the input admittance of a parallel RLC bandpass filter to determine its resonant frequency and bandwidth.
- Determining the susceptance needed from a shunt capacitor or inductor to match transmission line impedance in RF engineering.
- Analyzing power factor correction requirements by calculating the reactive susceptance of industrial motor loads.

## Frequently asked questions

### What is the difference between impedance and admittance?

Impedance (Z) measures the opposition to electrical current in an AC circuit, while admittance (Y) is the reciprocal of impedance (Y = 1/Z) and measures how easily current flows.

### Can I calculate admittance if one of the R, L, or C components is missing?

Yes, the calculator supports any subset of R, L, and C. You only need to provide at least one component value along with the frequency.

### What do positive and negative susceptance values indicate?

A positive susceptance (B > 0) indicates net capacitive behavior, while a negative susceptance (B < 0) indicates net inductive behavior.

### How does the topology setting affect the calculations?

In a series topology, the calculator first sums the impedances before taking the reciprocal. In a parallel topology, it directly sums the individual admittances of each branch.

### What unit is admittance measured in?

Admittance, conductance, and susceptance are all measured in Siemens (S), which is equivalent to reciprocal ohms (Ω⁻¹).

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