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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, and R and L cannot be negative. With L = 0 there is no resonance, so the resonant frequency shows "—" while the rest is still calculated. 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.

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Comments (1)

  • Editorial team

    The tool gives only the size of the impedance, but the two reactances shown beside it tell you the rest: when the inductive one is smaller the circuit behaves capacitively, when larger inductively. A neat self-test is to enter the resonant frequency it reports as the frequency: the two reactances become equal and the impedance falls to your resistance value. What frequency range are you designing for?

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