Calculate the complex impedance of series or parallel RLC, RL, RC and LC circuits at any frequency. Get |Z|, the phase angle, rectangular form, resonant frequency, Q factor and bandwidth, plus current and power if you enter a voltage.
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Connection
V
Adds current and power
Enter your values to see the result.
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How to use the RLC Impedance Calculator
Pick series or parallel and which components are in the circuit.
Enter R, L, C and the frequency with their units.
Read |Z| and the phase angle; a positive angle means inductive, negative means capacitive.
Check the resonant frequency and Q for circuits with both L and C.
Optionally enter the voltage to get current and power, then look at the sweep chart.
Impedance formulas
Circuit
Impedance
Magnitude |Z|
Series RL
R + jωL
√(R² + X_L²)
Series RC
R − j/(ωC)
√(R² + X_C²)
Series RLC
R + j(X_L − X_C)
√(R² + (X_L − X_C)²)
Parallel RL
1 ÷ (1/R − j/X_L)
R·X_L ÷ √(R² + X_L²)
Parallel RC
1 ÷ (1/R + j/X_C)
R·X_C ÷ √(R² + X_C²)
Parallel RLC
1 ÷ (1/R + j(ωC − 1/(ωL)))
1 ÷ √((1/R)² + (ωC − 1/(ωL))²)
X_L = 2πfL, X_C = 1/(2πfC), ω = 2πf. Phase angle θ = atan2(Im Z, Re Z); power factor = cos θ.
Series vs parallel at resonance
Property
Series RLC
Parallel RLC
Resonant frequency
f₀ = 1/(2π√(LC))
f₀ = 1/(2π√(LC))
|Z| at f₀
Minimum, equal to R
Maximum, equal to R
Current at f₀
Maximum
Minimum
Below f₀ the circuit is
Capacitive
Inductive
Above f₀ the circuit is
Inductive
Capacitive
Quality factor
Q = (1/R)√(L/C)
Q = R√(C/L)
All components are treated as ideal. Real inductors have series resistance and capacitors have ESR, which lower the Q of a real circuit.
Frequently asked questions
How do you calculate the impedance of a series RLC circuit?
Z = R + j(X_L − X_C), where X_L = 2πfL and X_C = 1/(2πfC). The magnitude is |Z| = √(R² + (X_L − X_C)²) and the phase angle is θ = atan((X_L − X_C)/R). With R = 100 Ω, L = 10 mH and C = 1 µF at 1 kHz, X_L = 62.83 Ω and X_C = 159.15 Ω, so |Z| ≈ 138.8 Ω at −43.9°.
How do you calculate parallel RLC impedance?
Add admittances instead of impedances: Y = 1/R + j(ωC − 1/(ωL)), then Z = 1/Y. The magnitude is |Z| = 1 / √((1/R)² + (ωC − 1/(ωL))²).
What does the phase angle tell me?
It is the angle between voltage and current. A positive angle means the circuit is inductive (current lags), a negative angle means capacitive (current leads) and 0° means purely resistive. Its cosine is the power factor.
What happens at resonance?
At f₀ = 1/(2π√(LC)) the inductive and capacitive reactances are equal. In a series circuit they cancel, so |Z| drops to R and the current peaks. In a parallel circuit the impedance rises to its maximum (R, or infinity for an ideal LC).
What is the Q factor?
Q measures how sharp the resonance is. For a series RLC, Q = (1/R)√(L/C); for a parallel RLC, Q = R√(C/L). The −3 dB bandwidth is f₀ ÷ Q, so a higher Q means a narrower, more selective response.
Why is my impedance infinite?
An ideal parallel LC circuit with no resistance has zero admittance exactly at resonance, so its impedance is infinite. Real circuits always have some loss; add the parallel resistance to get a finite result.
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