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.
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Key facts
Category
Math & Numbers
Input types
select, number, checkbox
Output type
json
Sample coverage
4
API ready
Yes
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.
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
1Select the circuit topology (series or parallel) and input the values for resistance (R), inductance (L), and capacitance (C).
2Specify the operating frequency, or enable the frequency sweep option by entering the start frequency, end frequency, and number of sweep points.
3The calculator computes the inductive reactance (X_L = 2πfL) and capacitive reactance (X_C = 1/(2πfC)) for each frequency point.
4It 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.
Examples
1. Analyzing a Series RLC Circuit at Power Line Frequency
Electrical Engineering Student
Background
A student is analyzing a series RLC circuit in a lab experiment to verify theoretical calculations at a standard power line frequency of 50 Hz.
Problem
Calculate the total impedance and phase angle of a series circuit with a 100 Ω resistor, a 0.1 H inductor, and a 10 µF capacitor.
How to use
Set the topology to 'series', enter 100 for R, 0.1 for L, 0.00001 for C, and 50 for the frequency. Keep the frequency sweep disabled.
The calculator outputs a total impedance magnitude of approximately 303.82 Ω and a phase angle of -70.78°, indicating a capacitive dominant circuit.
2. Frequency Sweep of a Parallel RLC Circuit
Hardware Design Engineer
Background
An engineer is designing a parallel RLC tank circuit and needs to observe how the impedance changes across a frequency range from 50 Hz to 200 Hz.
Problem
Determine the impedance magnitude and phase angle at 4 discrete frequency points to locate the resonance region.
FAQ
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.
Set the topology to 'parallel', enter 100 for R, 0.05 for L, and 0.0001 for C. Enable the frequency sweep, setting the start frequency to 50, end frequency to 200, and points to 4.
The calculator generates a JSON array showing the transition from inductive impedance (positive phase angle) at 50 Hz to capacitive impedance (negative phase angle) at higher frequencies, with the impedance magnitude peaking near resonance.