Impedance Calculator
Calculate the total impedance of RLC circuits in series or parallel configurations. Enter resistance, inductance, capacitance, and frequency to find the complex impedance, magnitude, phase angle, and admittance. Perfect for electronics, audio, and RF applications.
What Is Impedance?
Impedance (Z) is the total opposition that a circuit presents to alternating current (AC). It is a complex quantity that combines both resistance (R) and reactance (X). While resistance opposes current flow in both DC and AC circuits, reactance only opposes AC and is caused by inductors and capacitors.
Impedance is expressed as a complex number:
Z = R + jX
Where:
R = Resistance (real part)
X = Reactance (imaginary part)
j = Imaginary unit (√-1)
Inductive Reactance: XL = 2πfL (positive, inductive)
Capacitive Reactance: XC = 1/(2πfC) (negative, capacitive)
This calculator determines the total impedance of series or parallel RLC circuits, including the magnitude, phase angle, resonant frequency, and admittance.
How Does the Impedance Calculator Work?
The calculator uses the following principles:
- Inductive Reactance: XL = 2πfL — increases with frequency.
- Capacitive Reactance: XC = 1/(2πfC) — decreases with frequency.
- Series Circuit: Z = R + j(XL − XC) — components are added directly.
- Parallel Circuit: 1/Z = 1/R + 1/jXL + 1/(-jXC) — conductances and susceptances are added.
- Resonance: Occurs when XL = XC, f0 = 1/(2π√(LC)).
- Admittance: Y = 1/Z = G + jB, where G is conductance and B is susceptance.
Why Use This Impedance Calculator?
- Two Circuit Configurations: Supports both series and parallel RLC circuits.
- Complete Results: Get complex impedance, magnitude, phase angle, reactance, resonant frequency, and admittance.
- Visual Representation: An impedance triangle chart shows the relationship between resistance, reactance, and impedance.
- Free & Private: No registration, no data storage.
- Mobile-Friendly: Works on any device.
❓ Impedance Calculator FAQ
What is impedance?
Impedance (Z) is the total opposition a circuit presents to alternating current. It combines resistance (R) and reactance (X) into a complex quantity: Z = R + jX.
What is the difference between resistance and impedance?
Resistance opposes current flow in both DC and AC circuits. Impedance is a broader concept that includes resistance and reactance, and it only applies to AC circuits. Impedance can vary with frequency, while resistance stays constant.
What is reactance?
Reactance is the opposition to current flow caused by inductors and capacitors in AC circuits. Inductive reactance (XL = 2πfL) increases with frequency. Capacitive reactance (XC = 1/(2πfC)) decreases with frequency.
How is impedance calculated in a series RLC circuit?
In a series RLC circuit, the total impedance is Z = R + j(XL − XC). The magnitude is |Z| = √(R² + (XL − XC)²).
How is impedance calculated in a parallel RLC circuit?
In a parallel RLC circuit, the total impedance is found using 1/Z = 1/R + 1/jXL + 1/(-jXC). The calculator handles the complex arithmetic for you.
What is the phase angle in an RLC circuit?
The phase angle (θ) is the angle between the voltage and current in an AC circuit. It is calculated as θ = arctan(X/R). A positive angle means the circuit is inductive; a negative angle means it is capacitive.
What is resonant frequency?
Resonant frequency (f0) is the frequency at which inductive reactance equals capacitive reactance (XL = XC). At resonance, the impedance is purely resistive, and the phase angle is zero. f0 = 1/(2π√(LC)).
What is admittance?
Admittance (Y) is the reciprocal of impedance: Y = 1/Z. It is measured in siemens (S) and represents how easily current flows through a circuit. Y = G + jB, where G is conductance and B is susceptance.
What is the difference between a series and a parallel RLC circuit?
In a series RLC circuit, all components are connected in a single path, and the same current flows through each. The total impedance is the sum of individual impedances. In a parallel RLC circuit, components are connected across the same voltage source, and the total impedance is found from the reciprocal of the sum of reciprocals.
What happens at resonance in an RLC circuit?
At resonance, the inductive and capacitive reactances cancel each other out (XL = XC). The impedance is purely resistive (minimum impedance in series, maximum impedance in parallel), and the circuit is said to be "tuned."
How does frequency affect impedance?
In an inductive circuit, impedance increases with frequency. In a capacitive circuit, impedance decreases with frequency. At resonance, impedance is at a minimum for series circuits and at a maximum for parallel circuits.
What is the quality factor (Q) of an RLC circuit?
The quality factor (Q) is a measure of the sharpness of resonance. For a series RLC circuit, Q = XL/R = XC/R at resonance. Higher Q means a narrower bandwidth and more selective frequency response.
Can I use this calculator for audio circuits?
Yes. This calculator is useful for audio crossover design, loudspeaker impedance analysis, and filter design. Enter the resistance, inductance, and capacitance values to find the impedance at specific audio frequencies.
Can I use this calculator for RF (radio frequency) circuits?
Yes. The calculator works at any frequency. For RF circuits, enter the frequency in hertz, and the calculator will compute the impedance of inductors and capacitors at that frequency.
What is the difference between impedance and resistance in AC circuits?
Resistance is a real number that opposes current flow. Impedance is a complex number that includes resistance and reactance. In AC circuits, impedance determines not only the magnitude of current but also the phase relationship between voltage and current.
What is the unit of impedance?
Impedance is measured in ohms (Ω), the same unit as resistance.
How do I calculate impedance from voltage and current?
Impedance is calculated as Z = V / I, where V is the RMS voltage and I is the RMS current. In AC circuits, both V and I are phasors (complex numbers).
What is the difference between impedance and admittance?
Impedance (Z) is the opposition to current flow, measured in ohms. Admittance (Y) is the ease with which current flows, measured in siemens (S). They are reciprocals: Y = 1/Z.