# RLC Impedance & Phase Angle Calculator

Compute complex impedance, magnitude |Z| and phase angle φ for series or parallel RLC circuits: X_L=2πfL, X_C=1/(2πfC), |Z|=√(R²+X²), φ=atan2(X,R). Supports any subset of R/L/C and an optional linear frequency sweep.

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

- **Category:** Math & Numbers

- **Keywords:** impedance, RLC, series, parallel, reactance, phase angle, inductive reactance, capacitive reactance, frequency sweep, AC circuits, electrical engineering

## Overview

The RLC Impedance & Phase Angle Calculator computes the complex impedance, magnitude, and phase angle for series or parallel AC circuits containing any combination of resistors, inductors, and capacitors. It calculates inductive and capacitive reactances based on your operating frequency and supports linear frequency sweeps to analyze circuit behavior across a range of frequencies.

## 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): Operating frequency (Hz). Also used as the single-point value when sweep is disabled.
- **Enable Frequency Sweep** (checkbox): If checked, sample N points from Sweep Start to Sweep End and return a curve array.
- **Sweep Start (Hz)** (number): Required when sweep is enabled.
- **Sweep End (Hz)** (number): Required when sweep is enabled.
- **Sweep Points** (number): Number of points in the sweep (2–50). Required when sweep is enabled.
- **Decimal Places** (number)

## When to use

- When designing or analyzing AC circuits containing resistors, inductors, or capacitors in series or parallel configurations.
- When you need to determine the phase shift or power factor angle between voltage and current at a specific operating frequency.
- When plotting or analyzing the frequency response of an RLC filter or resonant circuit using a linear frequency sweep.

## How it works

- Select the circuit topology (series or parallel) and input the values for resistance (R), inductance (L), and capacitance (C).
- Specify the operating frequency, or enable the frequency sweep option by entering the start frequency, end frequency, and number of sweep points.
- The calculator computes the inductive reactance (X_L = 2πfL) and capacitive reactance (X_C = 1/(2πfC)) for each frequency point.
- It combines these reactances with the resistance to output the complex impedance (Z), magnitude (|Z|), and phase angle (φ) in a structured JSON format.

## Use cases

- Calculating the input impedance and phase shift of a passive crossover network for audio speakers.
- Simulating the frequency response of a bandpass filter to determine its bandwidth and cutoff frequencies.
- Determining the impedance matching requirements for RF antennas or AC power distribution systems.

## Frequently asked questions

### Can I calculate the impedance of a circuit with only a resistor and a capacitor?

Yes, you can omit any component. The calculator supports any subset of R, L, and C.

### What is the difference between series and parallel topology in the calculations?

Series topology adds impedances directly (Z = R + j(X_L - X_C)), while parallel topology adds admittances (1/Z = 1/R + 1/(jX_L) + jX_C).

### How does the frequency sweep feature work?

When enabled, the calculator evaluates the circuit's impedance at multiple evenly spaced frequency points between your specified start and end frequencies.

### What units should I use for the component values?

Use Ohms (Ω) for resistance, Henries (H) for inductance, Farads (F) for capacitance, and Hertz (Hz) for frequency.

### Does this calculator provide the resonant frequency of the circuit?

It does not explicitly output the resonant frequency, but you can identify it by finding the frequency where the phase angle is zero or the impedance magnitude reaches its minimum or maximum.

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