RLC Resonance Calculator
Series RLC circuit at any frequency — resonant frequency, impedance magnitude and phase, reactances, current, Q, bandwidth and the voltages across L and C at resonance.
How it works
f₀ = 1 ÷ (2π√LC); X_L = 2πfL, X_C = 1 ÷ (2πfC); |Z| = √[R² + (X_L − X_C)²]; φ = atan[(X_L − X_C)/R]; Q = √(L/C) ÷ R
In a series RLC circuit the inductor’s reactance rises with frequency while the capacitor’s falls; where they are equal they cancel, the impedance drops to R alone and the current peaks — resonance. Below f₀ the capacitor dominates and current leads the voltage; above it the inductor dominates and current lags. At resonance the voltages across L and C are each Q times the source and opposite in phase, which is how a modest drive can produce dangerous voltages in a high-Q tank.
Worked example
50 Ω, 10 mH, 100 nF: f₀ = 5.03 kHz, Q = 6.3, bandwidth 796 Hz. Driven at 5.00 kHz the circuit is slightly capacitive (|Z| = 50.2 Ω, −5°) and 10 V pushes 199 mA — with 63 V across the inductor.
Frequently asked questions
Parallel RLC?
Same f₀, but impedance peaks instead of dipping and Q = R√(C/L); use the Q factor calculator’s parallel option.
Why is the phase angle sign important?
It tells you whether to add capacitance or inductance to bring a load to unity power factor.
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This calculator is for educational purposes. Double-check important results before acting on them.