RLC Impedance Calculator
A series RLC circuit combines a resistor, an inductor, and a capacitor in one loop. Its opposition to alternating current, the impedance, depends on frequency because inductive and capacitive reactances change with frequency. Enter the resistance, inductance, capacitance, and the operating frequency to find the inductive reactance, capacitive reactance, total impedance magnitude, phase angle, and the resonant frequency where the reactances cancel.
Series RLC impedance formula
XL = 2 * pi * f * L
XC = 1 / (2 * pi * f * C)
Z = sqrt( R2 + (XL - XC)2 )
Phase = arctan( (XL - XC) / R )
Resonant frequency f0 = 1 / (2 * pi * sqrt(L * C))
At resonance XL equals XC, the reactive parts cancel, Z equals R, and the phase angle is zero.
Worked example
With R = 100 ohms, L = 0.05 H, C = 0.000001 F, at f = 1,000 Hz: XL = 2 pi * 1000 * 0.05 = 314.16 ohms. XC = 1 / (2 pi * 1000 * 0.000001) = 159.15 ohms. Z = sqrt(100^2 + (314.16 - 159.15)^2) = sqrt(10,000 + 24,028) = 184.47 ohms. Phase = arctan(155.01 / 100) = 57.18 degrees (inductive). Resonant frequency = 1 / (2 pi sqrt(0.05 * 0.000001)) = 711.76 Hz.
RLC impedance: frequently asked questions
How is series RLC impedance calculated?
For a series RLC circuit, impedance magnitude is Z = sqrt(R2 + (XL - XC)2), where XL = 2 pi f L is the inductive reactance and XC = 1 / (2 pi f C) is the capacitive reactance. The phase angle is arctan((XL - XC) / R).
What is the resonant frequency?
Resonance occurs where inductive and capacitive reactances cancel: f0 = 1 / (2 pi sqrt(L C)). At resonance the impedance equals the resistance R and the phase angle is zero.
What units should I enter?
Resistance in ohms, inductance in henries, capacitance in farads, and frequency in hertz. For typical components convert first: a 10 microfarad capacitor is 0.00001 F, and a 1 millihenry inductor is 0.001 H.
What does a positive or negative phase angle mean?
A positive phase angle means the circuit is inductive (current lags voltage). A negative phase angle means it is capacitive (current leads voltage). Zero phase means the circuit is at resonance and behaves resistively.
Sources
- NIST: SI units (ohm, henry, farad, hertz).
- The series RLC impedance, phase, and resonance formulas are standard results of AC circuit theory.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.