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RLC Impedance Calculator

Impedance combines resistance and net reactance into one complex quantity. Its magnitude sets the current; its angle sets the phase between voltage and current, which is what power factor measures.

Series RLC Impedance — Z = √(R² + (Xʟ − X꜀)²)

Impedance, phase angle and power factor of a series R-L, R-C or R-L-C circuit. Leave L or C blank if the circuit doesn't have it.

Inductive reactance Xʟ
Impedance Z
Phase angle φ
Power factor cos φ
Circuit behaves as
Impedance triangle
R = 3 ΩX = 3.9992 Ωφ=53.1°Z = 4.9994 Ω
  1. 1.Given: f = 50 Hz, R = 3 Ω, L = 12.73 mH
  2. 2.FormulaXʟ = 2πfLSubstituteXʟ = 2π × 50 × 0.0127ResultXʟ = 3.9992 Ω
  3. 3.FormulaX = Xʟ − X꜀ (net reactance)SubstituteX = 3.9992 − 0ResultX = 3.9992 Ω
  4. 4.FormulaZ = √(R² + X²)SubstituteZ = √(3² + 3.9992²)ResultZ = 4.9994 Ω
  5. 5.Formulaφ = tan⁻¹(X ÷ R)Substituteφ = tan⁻¹(3.9992 ÷ 3)Resultφ = 53.1249°
  6. 6.Formulacos φ = R ÷ Z (power factor)Substitutecos φ = 3 ÷ 4.9994Resultcos φ = 0.6001
Common trap: Impedances don't add like resistances — R and X are at 90° to each other, so a 3 Ω resistor in series with 4 Ω of reactance gives 5 Ω, not 7 Ω. Always add them as a right triangle (phasor sum), never arithmetically.

The formula

Z = √(R² + (X_L − X_C)²) ; φ = arctan((X_L − X_C) / R)

Z
impedance magnitude (ohms)
R
resistance (ohms)
X_L, X_C
inductive and capacitive reactance at this frequency (ohms)
φ
phase angle between voltage and current (degrees)

Worked example

R = 100 Ω, L = 100 mH, C = 10 µF at 50 Hz.

  1. X_L = 2π × 50 × 0.1 = 31.4 Ω ; X_C = 1/(2π × 50 × 10⁻⁵) = 318.3 Ω
  2. Net reactance: X = 31.4 − 318.3 = −286.9 Ω (capacitive)
  3. Z = √(100² + 286.9²) = √(10000 + 82312)
  4. φ = arctan(−286.9 / 100) = −70.8°

Z = 303.8 Ω at −70.8°: the current leads the voltage, so the circuit is capacitive.

Where you'll use it

AC circuit analysis, filter response, and working out the current a mains-connected load will draw. A negative angle means leading current (capacitive); positive means lagging (inductive), which is the normal case for motors.

The laws behind it

Parts this applies to

Resistor (fixed)Potentiometer / Rheostat / TrimmerResistor Array / NetworkThermistor (NTC / PTC)Varistor / MOVSupercapacitorLED (light-emitting diode)MOSFET

Related calculators

Capacitive and Inductive Reactance CalculatorX_C = 1 / (2πfC)LC Resonance Calculatorf₀ = 1 / (2π√(LC))Power Triangle CalculatorS² = P² + Q²Power Factor Correction CalculatorQ_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf)