Calculators
Impedance Calculator
Calculate series AC impedance, reactance, phase angle, and resonance.
Impedance Calculator tool
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About This Tool
Impedance describes how a circuit opposes alternating current by combining ordinary resistance with frequency-dependent reactance. This calculator models an ideal series circuit containing a resistor, inductor, capacitor, or any useful combination of them. Enter R, L, C, and frequency to find impedance magnitude, rectangular form, phase angle, individual reactances, power factor, and the ideal resonant frequency when both L and C are present. Calculations run locally in your browser.
How To Use It
- Enter resistance R in ohms. Use 0 if there is no resistor.
- Enter inductance L and capacitance C with their engineering units. Use 0 for a component that is not present, such as C = 0 for an RL circuit.
- Enter the AC operating frequency and choose Hz, kHz, or MHz.
- Read the impedance magnitude, net reactance, phase angle, power factor, and resonance information. Negative phase indicates net capacitive behavior; positive phase indicates net inductive behavior.
Examples
Series RC circuit
For R = 100 Ω, C = 1 µF, L = 0, and f = 1 kHz, XC is about 159.15 Ω. The impedance magnitude is about 188 Ω and the negative phase angle indicates capacitive behavior.
Series RL circuit
For R = 100 Ω, L = 10 mH, C = 0, and f = 1 kHz, XL is about 62.83 Ω. The impedance magnitude is about 118.1 Ω and the positive phase angle indicates inductive behavior.
Series RLC near resonance
With both L and C present, XL and XC oppose each other. At the ideal resonant frequency f0 = 1/(2π√LC), they are equal, net reactance approaches zero, and series impedance approaches R.
Useful Notes
Series impedance formula
For an ideal series RLC circuit, Z = R + j(XL − XC), where XL = 2πfL and XC = 1/(2πfC). The impedance magnitude is |Z| = √(R² + (XL − XC)²).
Phase angle and circuit behavior
The phase angle is θ = atan2(XL − XC, R). A positive angle means the circuit is net inductive, a negative angle means it is net capacitive, and an angle near zero means the impedance is approximately resistive at that frequency.
Power factor
For this ideal series model, power factor magnitude is R/|Z|, equivalent to cos(θ). It describes how much of the impedance magnitude lies on the resistive axis; this calculator does not estimate real-world losses or utility billing effects.
Resonant frequency
When both L and C are greater than zero, ideal series resonance occurs at f0 = 1/(2π√LC). At resonance XL equals XC, their reactances cancel, the phase angle is zero, and the impedance magnitude equals the series resistance.
RC and RL circuits
The same series formula covers simpler circuits. Set L to 0 for an RC circuit or C to 0 for an RL circuit. Setting a component to zero means that component is absent; it is not treated as a physical zero-valued capacitor or inductor.
Ideal-model limitations
Real inductors and capacitors have winding resistance or ESR, parasitic elements, tolerance, dielectric or core losses, and self-resonant limits. At high frequencies or near component self-resonance, measured impedance can differ substantially from this ideal lumped-element calculation.
FAQ
What is the difference between resistance and impedance?
Resistance is the real, dissipative part of opposition to current. Impedance is the broader AC quantity that combines resistance with inductive or capacitive reactance and therefore has both magnitude and phase.
Can I calculate an RC or RL circuit?
Yes. Set the missing reactive component to 0. Use L = 0 for series RC or C = 0 for series RL.
Does this calculate parallel RLC impedance?
No. This page intentionally models series circuits, where impedances add directly. Parallel RLC circuits require adding admittances and use different relationships.
Why can the phase angle be negative?
A negative phase angle means capacitive reactance is larger than inductive reactance at the selected frequency, so the circuit is net capacitive. A positive angle means it is net inductive.
Is resonance always exactly where a real circuit peaks or dips?
Not necessarily. The displayed resonance is for ideal L and C values. Component losses, parasitics, source/load impedance, and topology can shift or broaden real measured behavior.