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RLC Impedance Calculator

Find the impedance of a series RLC circuit.

How it is calculated

For a series RLC circuit at angular frequency ω = 2πf, the inductor has reactance XL = ωL and the capacitor XC = 1 ÷ (ωC). The impedance is Z = √(R² + (XL − XC)²). The tool also gives the resonant frequency f0 = 1 ÷ (2π√(LC)), at which XL = XC and the impedance falls to just R. Enter R in ohms, L in henries, C in farads and f in hertz, so a 10 mH coil is 0.01 and a 1 µF capacitor is 0.000001. C and f must be above zero. The tool gives only the magnitude of Z, not the phase angle.

Worked example

Take R = 50 Ω, L = 0.01 H, C = 0.000001 F and f = 1000 Hz. Angular frequency: ω = 2π × 1000 ≈ 6283.2. Inductive reactance: 6283.2 × 0.01 = 62.83 Ω. Capacitive reactance: 1 ÷ (6283.2 × 0.000001) = 159.15 Ω. Net reactance: 62.83 − 159.15 = −96.32 Ω. Impedance: √(50² + 96.32²) = 108.53 Ω. The resonant frequency is 1,591.55 Hz.

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Common mistakes

  • Entering L in millihenries or C in microfarads without converting. The fields take henries and farads, so 1 µF must be typed as 0.000001.
  • Entering the frequency in kilohertz or as angular frequency ω. The field expects ordinary hertz.
  • Simply adding R, XL and XC. The reactances are 90° out of phase with the resistance and with opposite signs, so they combine by the square-root formula.
  • Assuming the impedance is smallest at your chosen frequency. It is smallest at the resonant frequency, where it equals R.
  • Applying the result to a parallel RLC circuit. The formulas here are for series only.

About this calculator

In a series RLC circuit, the total opposition to alternating current — the impedance — combines resistance with reactance: Z = √(R² + (X_L − X_C)²), where the inductive reactance X_L = 2πfL grows with frequency and the capacitive reactance X_C = 1/(2πfC) shrinks with frequency. At the resonant frequency f₀ = 1/(2π√(LC)), the two reactances cancel exactly, leaving impedance at its minimum (equal to just R) and current at its maximum.

Electrical and electronics engineers use this calculation to design radio tuners, band-pass filters, and oscillator circuits, and to predict how a circuit responds across a range of AC frequencies. Enter the resistance, inductance, capacitance, and operating frequency to find the reactances, total impedance, and resonant frequency of the circuit.

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