About the RLC Impedance Calculator
This RLC impedance calculator works out the total impedance of a resistor, inductor and capacitor connected either in series or in parallel, at the frequency you choose. It returns the impedance magnitude |Z| in ohms, the phase angle between voltage and current, the individual inductive and capacitive reactances, the rectangular form R + jX, the current drawn from a given AC voltage, and the resonant frequency of the L–C pair.
It is useful for electronics students checking homework, technicians sizing filters, crossovers and snubbers, and engineers estimating how a load behaves on an AC supply. Leave L or C at zero to analyse simpler RL, RC or LC circuits — a zero value means that component is simply not in the circuit.
The math assumes ideal components: pure resistance, an inductor with no winding resistance and a capacitor with no leakage or ESR. A sweep chart shows how |Z| changes over two decades around your frequency, so you can see the dip (series) or peak (parallel) at resonance.
With the default inputs, the impedance |z| is 138.846 Ω. Change any value above to recalculate instantly.
How to use the rlc impedance calculator
- 1Choose whether the components are in series or in parallel.
- 2Enter R in ohms, L in millihenries and C in microfarads (0 removes a part).
- 3Enter the operating frequency and, optionally, the source voltage.
- 4Read |Z|, the phase angle and the rectangular form R + jX.
- 5Check the sweep chart to see where resonance falls relative to your frequency.
Formula and method
Inductors and capacitors oppose AC with reactance that depends on frequency: XL = 2πfL rises with frequency while XC = 1/(2πfC) falls. In a series circuit the reactances subtract and combine with the resistance at right angles, so |Z| = √(R² + X²) with X = XL − XC, and the phase angle is atan(X/R).
In a parallel circuit the calculator adds admittances instead: conductance G = 1/R and susceptance B = ωC − 1/XL, then Z = 1/(G + jB), giving |Z| = 1/√(G² + B²) and φ = −atan(B/G). Resonance occurs at f0 = 1/(2π√(LC)), where XL = XC. Components are ideal; a value of zero removes that component from the circuit.
- R
- Resistance (Ω)
- L
- Inductance (H; entered in mH)
- C
- Capacitance (F; entered in µF)
- f, ω
- Frequency in Hz and angular frequency 2πf
- XL, XC
- Inductive and capacitive reactance (Ω)
- φ
- Phase angle of the impedance
- f0
- Resonant frequency
Worked examples
Series 100 Ω, 10 mH, 1 µF at 1 kHz
XL = 2π × 1000 × 0.01 = 62.83 Ω and XC = 1/(2π × 1000 × 1e−6) = 159.15 Ω, so the net reactance is −96.32 Ω. |Z| = √(100² + 96.32²) ≈ 138.85 Ω at −43.9°, a capacitive circuit. 10 V drives about 72 mA.
Motor-style RL load with a 10 µF capacitor at 60 Hz
At 60 Hz, XL = 37.70 Ω and XC = 265.26 Ω, a net −227.56 Ω. With 50 Ω of resistance, |Z| = √(50² + 227.56²) ≈ 232.99 Ω and the phase is −77.6°, so the capacitor dominates far below the 159 Hz resonance.
Parallel 1 kΩ, 10 mH, 1 µF at 1 kHz
G = 1/1000 = 0.001 S and B = ωC − 1/XL = 0.006283 − 0.015915 = −0.009632 S. |Z| = 1/√(0.001² + 0.009632²) ≈ 103.26 Ω with a +84.1° phase: below resonance the inductor carries most of the current, so the parallel circuit looks inductive.
Frequently asked questions
What is impedance in an RLC circuit?+
Impedance is the total opposition to alternating current, combining resistance with the reactance of inductors and capacitors. It is a complex quantity with a magnitude in ohms and a phase angle, written Z = R + jX.
What happens at resonance?+
At f0 = 1/(2π√LC) the inductive and capacitive reactances are equal and cancel. A series RLC circuit then has its minimum impedance (just R) and maximum current; a parallel circuit has its maximum impedance.
What does a negative phase angle mean?+
A negative phase angle means the circuit is capacitive: current leads the voltage. A positive angle means it is inductive and current lags the voltage. Zero means it behaves like a pure resistor.
How do I calculate an RC or RL circuit with this tool?+
Set the unused component to zero. With L = 0 you get a series or parallel RC circuit; with C = 0 you get an RL circuit. Zero means the part is absent, not a short.
Why does impedance change with frequency?+
Inductive reactance grows in proportion to frequency (XL = 2πfL) while capacitive reactance shrinks (XC = 1/2πfC). Only the resistor is frequency-independent, so the overall impedance varies with frequency.