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LC Resonance Calculator

At one particular frequency the inductive and capacitive reactances are equal and cancel. A series circuit then looks purely resistive and draws maximum current; a parallel circuit blocks. Every tuned circuit, oscillator and filter starts here.

LC Resonance — f₀ = 1 / (2π√(LC))

Resonant frequency of an LC circuit. Add the series resistance to also get the Q factor and bandwidth of a series RLC circuit.

Resonant frequency f₀
Characteristic impedance √(L/C)
  1. 1.Given: L = 100 µH, C = 100 pF
  2. 2.Formulaf₀ = 1 ÷ (2π√(LC))Substitutef₀ = 1 ÷ (2π × √(100e-6 × 100e-12))Resultf₀ = 1.5915 MHz
  3. 3.FormulaZ₀ = √(L ÷ C)SubstituteZ₀ = √(100e-6 ÷ 100e-12)ResultZ₀ = 1000 Ω
Common trap: At resonance Xʟ and X꜀ are equal and cancel— they don't disappear. A series RLC circuit drops to its minimum impedance (just R, maximum current); a parallel LC tank does the opposite and peaks at maximum impedance. Same f₀, opposite behavior.

The formula

f₀ = 1 / (2π√(LC)) ; Z₀ = √(L/C) ; Q = Z₀/R ; BW = f₀/Q

f₀
resonant frequency (hertz)
L
inductance (henries)
C
capacitance (farads)
Q
quality factor — sharpness of the resonance (dimensionless)
BW
−3 dB bandwidth around f₀ (hertz)

Worked example

L = 100 mH, C = 10 µF, with 10 Ω of series resistance.

  1. LC = 0.1 × 10 × 10⁻⁶ = 1 × 10⁻⁶, so √(LC) = 1 × 10⁻³
  2. f₀ = 1 / (2π × 10⁻³) = 159.2 Hz
  3. Z₀ = √(0.1 / 10⁻⁵) = √10000 = 100 Ω
  4. Q = 100 / 10 = 10, so BW = 159.2 / 10 = 15.9 Hz

f₀ = 159.2 Hz with Q = 10 and a 15.9 Hz bandwidth.

Where you'll use it

Radio tuning, filter and oscillator design, and the exam favourite about current at resonance in a series RLC circuit. Lower series resistance means higher Q and a sharper, narrower peak.

The laws behind it

Parts this applies to

Inductor / CoilChoke / Common-mode ChokeSwitching Regulator (Buck/Boost)Stepper MotorSMPS / Power SupplyDC-DC Converter (buck/boost module)BLDC MotorFluorescent Tube / CFL

Related calculators

Capacitive and Inductive Reactance CalculatorX_C = 1 / (2πfC)RLC Impedance CalculatorZ = √(R² + (X_L − X_C)²)RC Time Constant Calculatorτ = R × CPower Triangle CalculatorS² = P² + Q²