Circuit Analysis & FundamentalsDesign workbench
AC Impedance & Phasor Calculator
Complex impedance of a series or parallel R-L-C combination at a chosen frequency — magnitude, phase, and both rectangular and polar forms, with the impedance-vs-frequency curve.
About this calculator
In AC circuits, resistance generalises to impedance — a complex number that captures both how much a circuit opposes current and how far it shifts the phase between voltage and current. This calculator computes the impedance of a series or parallel resistor-inductor-capacitor combination at a frequency you choose, and presents it every way engineers need it: magnitude and phase angle, real (resistance) and imaginary (reactance) parts, and the equivalent rectangular (a + jb) and polar (|Z|∠θ) phasor forms.
The physics is in the reactances. An inductor's reactance X_L = ωL rises with frequency and adds a +90° phase (its impedance is +jωL); a capacitor's reactance X_C = 1/(ωC) falls with frequency and adds a −90° phase (its impedance is −j/ωC). In a series R-L-C the net reactance is X_L − X_C, so the circuit looks inductive above its resonant frequency and capacitive below it; at resonance the reactances cancel and the impedance collapses to just R. A parallel combination behaves as the dual. The tool applies ω = 2πf, combines the elements for the topology you select, and plots how the impedance magnitude varies with frequency so you can see the resonant dip (series) or peak (parallel) and where your chosen frequency sits on it.
Use it to check a filter's impedance at a frequency of interest, to see whether a network looks inductive or capacitive at the operating point, or to convert cleanly between rectangular and polar phasor forms. It models ideal elements at a single frequency; for the full frequency response of a filter, see the filter and frequency-response tools it cross-links to.
Design notes & common mistakes
- Inductor impedance is +jωL (angle +90°); capacitor impedance is −j/(ωC) (angle −90°). The signs are the whole story of the phase.
- Series R-L-C net reactance is X_L − X_C: inductive above resonance, capacitive below, purely R at resonance.
- Polar form (|Z|∠θ) is easiest for multiplying/dividing phasors; rectangular (a + jb) is easiest for adding series impedances. Convert freely.
- A phase near ±90° means an almost-lossless reactive network; a phase near 0° means resistance dominates at this frequency.
Assumptions
- Ideal R, L, and C with no parasitics; impedance evaluated at the single stated frequency.
- Steady-state sinusoidal (phasor) analysis, angular frequency ω = 2πf.
- Inductive reactance +jωL and capacitive reactance −j/(ωC); passive sign convention.
When to use this calculator
Appropriate for
- Finding the impedance magnitude and phase of an R-L-C network at a specific frequency
- Checking whether a network looks inductive or capacitive at the operating point
- Converting between rectangular and polar phasor impedance forms
Not suitable for
- Full frequency response or filter transfer functions (use the first/second-order filter tools)
- Networks with more than one series or parallel R-L-C group without hand reduction
- Real components where parasitics and self-resonance dominate the impedance
What this calculator does not cover
- Ideal elements at one frequency — no ESR, ESL, dielectric loss, or self-resonance of real parts is included.
- Single series or single parallel R-L-C group; arbitrary ladder or bridge networks are not reduced here.
- Steady-state sinusoidal analysis only; it says nothing about transient or switching behaviour.
- Gives the impedance phasor, not a transfer function or full Bode response across frequency (use the filter tools).
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
What is impedance, and how does it differ from resistance?
Impedance is the AC generalisation of resistance: a complex number Z = R + jX whose magnitude sets how much the circuit opposes current and whose angle sets the phase shift between voltage and current. Resistance is just the real part; the imaginary part, reactance, comes from inductors and capacitors and is what makes the phase non-zero.
What are the impedances of an inductor and a capacitor?
An inductor has impedance +jωL, so its reactance X_L = ωL grows with frequency and it adds +90° of phase. A capacitor has impedance −j/(ωC), so its reactance X_C = 1/(ωC) shrinks with frequency and it adds −90° of phase. Here ω = 2πf is the angular frequency.
How do I know if a circuit is inductive or capacitive?
Look at the sign of the reactance (the imaginary part of Z) or the phase angle. A positive reactance and positive phase mean the circuit is net inductive and current lags the voltage; a negative reactance and negative phase mean it is net capacitive and current leads. At the resonant frequency the two cancel and the impedance is purely resistive.
References
- Nilsson, J. & Riedel, S., Electric Circuits, 11th ed. (phasors and impedance)
- Sadiku, M., Fundamentals of Electric Circuits, 6th ed. (sinusoidal steady-state analysis)
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