RLC Circuit Calculator — Damping & Natural Frequency
Enter resistance, inductance and capacitance to find the natural frequency, damping coefficient, quality factor, and transient response type (underdamped, critically damped or overdamped) of a series RLC circuit.
Ω
H
F
Frequency where inductive and capacitive reactance cancel
- 1
LC product
0.001 × 0.000001 = 0.000000001 - 2
Angular frequency ω₀
1 ÷ √(0.000000001) = 31,622.78 rad/s - 3
Natural frequency f₀
31,622.78 ÷ (2π) = 5,032.921
How does this calculator work?
Enter R, L and C (SI units). Natural frequency ω₀ = 1/√(LC); damping ratio ζ = (R/2)√(C/L); quality factor Q = (1/R)√(L/C). ζ < 1 → underdamped (oscillatory); ζ = 1 → critically damped (fastest settling); ζ > 1 → overdamped (no ringing).
Formula
How this is calculated
A series RLC circuit has three fundamental parameters that determine how it responds to a sudden change (step input or impulse). The natural frequency ω₀ = 1/√(LC) is the frequency at which inductive and capacitive reactances cancel. The damping coefficient α = R/(2L) quantifies how quickly oscillations decay — higher R dissipates energy faster. Together they produce the damping ratio ζ = α/ω₀: when ζ < 1 the circuit is underdamped and oscillates at the damped frequency ωd = √(ω₀² − α²), ringing before settling; when ζ = 1 it is critically damped, settling fastest without overshoot; when ζ > 1 it is overdamped, settling slowly without oscillation.
The quality factor Q = 1/(2ζ) = (1/R)√(L/C) measures how selective the resonance is. A high Q (small R relative to √(L/C)) gives a sharp, narrow resonance peak and the bandwidth f₀/Q is correspondingly narrow. The characteristic impedance Z₀ = √(L/C) is the common reactance value of L and C at resonance.
This model assumes a series topology with ideal, linear components (no core saturation, no ESR on the capacitor, no parasitic capacitance). Real inductors have series resistance (DCR) that adds to R; including it in the R field improves accuracy. Use consistent SI units: H for inductance, F for capacitance, Ω for resistance.
Frequently asked questions
An underdamped circuit (ζ < 1) oscillates, with voltage crossing zero multiple times before settling — useful in oscillators and filters, but can cause instability in power converters. An overdamped circuit (ζ > 1) discharges without crossing zero, settling more slowly. Critically damped (ζ = 1) is the fastest non-oscillatory response.
The natural frequency ω₀ = 1/√(LC) depends only on the reactive components. Resistance changes the damping ratio and bandwidth (the width of the resonance peak) but not its centre frequency. In a parallel RLC circuit the relationship is the same.
The calculator expects SI: henries (H), farads (F), ohms (Ω). Convert: 1 mH = 0.001 H; 47 µH = 4.7e-5 H; 1 µF = 1e-6 F; 100 nF = 1e-7 F; 10 pF = 1e-11 F.
Also known as
TG we-Calculate Editorial Team. (2026). RLC Circuit Calculator — Damping & Natural Frequency [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rlc-circuit-calculator
TG we-Calculate Editorial Team. "RLC Circuit Calculator — Damping & Natural Frequency." TG we-Calculate. 2026. https://we-calculate.com/calculator/rlc-circuit-calculator.
TG we-Calculate Editorial Team, "RLC Circuit Calculator — Damping & Natural Frequency," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rlc-circuit-calculator
@misc{wecalculate_rlc_circuit_calculator, title = {RLC Circuit Calculator — Damping & Natural Frequency}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rlc-circuit-calculator}}, year = {2026}, note = {TG we-Calculate} }
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