RLC Circuit Calculator — Resonant Frequency, Q Factor, Bandwidth and Impedance

Background.

Connect an inductor to a capacitor and you have built something that wants to oscillate. Energy held in the capacitor's electric field drains into the inductor's magnetic field and back again, at a rate fixed by the two component values alone. Add resistance and some of that energy turns into heat on every swing. Those three ingredients are behind the tuned stage of a radio receiver, the LC filter on a switching regulator's output, the tank of an oscillator, and the ringing on a scope trace when a fast edge meets stray inductance and capacitance.

Give this calculator R, L and C with their units, say whether they are wired in series or as a parallel tank, and it reports the natural frequency f₀, the quality factor Q, the −3 dB bandwidth and its two edges, the damping ratio, and the frequency a disturbance actually rings at. A second group of outputs describes the circuit at a frequency you choose: the impedance magnitude, its phase angle, and the inductive and capacitive reactances. A one-line reading of the damping sums up whether the circuit rings or settles.

The topology choice changes more than people expect, because resistance plays opposite roles in the two arrangements. In series, current flows through R, so a smaller resistance means less loss and a sharper peak. In a parallel tank, R is a path across the tank that bleeds energy away, so a larger resistance means a sharper peak. With the default 100 mH and 10 µF, a 10 Ω resistor gives Q = 10 in series but only 0.1 in parallel; the parallel tank needs 1 kΩ to match.

Everything assumes ideal components. Real coils have winding resistance, core loss and a self-resonant frequency of their own, and class-2 ceramic capacitors lose a large share of their marked value under DC bias. Those effects shift a physical resonance by percentages, so read the long decimal tails as arithmetic, not as a prediction of what a bench measurement will show.

What is rlc circuit calculator?

An RLC circuit combines resistance, inductance and capacitance, and because it has two places to store energy it is a second-order system: it can oscillate. Resonance is the frequency at which the inductor's reactance, which rises with frequency, exactly equals the capacitor's, which falls, so the two cancel and the network behaves like the bare resistance. The quality factor Q measures how sharp that resonance is. It has two equivalent readings: the resonant frequency divided by the bandwidth between the half-power points, and 2π times the energy stored divided by the energy lost per cycle. The damping ratio ζ = 1/(2Q) describes the same property in time: below 1 a disturbance rings while decaying, at exactly 1 the circuit is critically damped and settles as fast as possible without overshoot, and above 1 it is overdamped and returns slowly without oscillating.

How to use this calculator.

1. 01Pick the topology. Series means one current flows through all three parts; parallel means all three share one voltage, with R connected across the inductor and capacitor.
2. 02For a parallel tank, make sure R is the load or loss across the tank. If your resistance is the coil's own winding resistance, sitting in series with the inductor inside a parallel circuit, that arrangement is not modelled and its resonance is lower.
3. 03Enter R, L and C with their unit menus — Ω, kΩ or MΩ; nH, µH, mH or H; pF, nF, µF, mF or F. Each value must be greater than zero.
4. 04Set the analysis frequency to the frequency of the signal you care about: the impedance, phase and two reactances are reported there. It has no effect on f₀, Q, bandwidth or damping, which belong to the components alone.
5. 05Use Q and the bandwidth to judge selectivity, and the damping ratio to judge transient behaviour. The sign of the phase tells you whether the circuit looks inductive or capacitive at your chosen frequency.

The formula.

Resonance comes from setting the two reactances equal, 2πfL = 1/(2πfC), which gives f₀ = 1/(2π√(LC)) with L in henries and C in farads. Resistance does not appear, so R moves the sharpness of the peak but never its position. A useful intermediate is the characteristic impedance Z₀ = √(L/C), the reactance of either part at f₀. The quality factors are then simple ratios: Q = Z₀/R in series and Q = R/Z₀ for the ideal parallel tank, so for the same three parts the two Q values multiply to exactly 1. The damping ratio is ζ = 1/(2Q) and the bandwidth is BW = f₀/Q. The half-power edges are computed exactly, f₁,₂ = f₀(√(1 + 1/(4Q²)) ∓ 1/(2Q)), rather than as the textbook shortcut f₀ ± BW/2 that Fiore's text gives for higher-Q circuits. The exact pair always differs by f₀/Q and always multiplies to f₀², because resonance is the geometric mean of the two edges; the shortcut drifts at moderate Q and goes negative below Q = 0.5. A step or pulse makes an underdamped circuit ring at f_d = f₀√(1 − ζ²), and at or above ζ = 1 the damped frequency is reported as zero because nothing oscillates. Impedance follows OpenStax: X_L = 2πfL and X_C = 1/(2πfC); in series Z = R + j(X_L − X_C), with |Z| = √(R² + (X_L − X_C)²) and phase arctan((X_L − X_C)/R). For the parallel tank the same algebra runs on admittance, Y = 1/R + j(2πfC − 1/(2πfL)), and |Z| = 1/|Y|. Phase is voltage relative to current: positive means inductive, negative capacitive. Left out of the model are winding resistance, core and dielectric loss, capacitor ESR and ESL, skin effect and inductor self-resonance.

A worked example.

Frequently asked questions.

References& sources.

1. [1]James M. Fiore, AC Electrical Circuit Analysis: A Practical Approach, §8.2 'Series Resonance' (Engineering LibreTexts). Source of f₀ = 1/(2π√LC) (Eq. 8.2), the series quality factor as Q = X₀/R_T (Eq. 8.12) and Q = (1/R_T)√(L/C) (Eq. 8.13), and the bandwidth relations BW = f₂ − f₁ with Q = f₀/BW (Eq. 8.3/8.4). Also the source of the half-power approximations f₁ ≈ f₀ − BW/2 and f₂ ≈ f₀ + BW/2 (Eq. 8.10/8.11), printed as valid for higher-Q circuits — this page computes the exact form instead and says so. Open access; retrieved 2026-07-29.
2. [2]James M. Fiore, AC Electrical Circuit Analysis: A Practical Approach, §8.3 'Parallel Resonance' (Engineering LibreTexts). Source of the parallel quality factor Q = R_T/X_L (Eq. 8.19) and Q = R_T√(C/L) (Eq. 8.20), and of Eq. 8.21 f₀ = (1/2π√LC)√(1 − CR²/L) for the parallel topology in which R is in series with the coil — the arrangement this page explicitly does not model. Open access; retrieved 2026-07-29.
3. [3]OpenStax (Rice University), University Physics Volume 2, §15.3 'RLC Series Circuits with AC'. Source of X_C = 1/(ωC) (Eq. 15.3), X_L = ωL (Eq. 15.8), the phase φ = tan⁻¹((X_L − X_C)/R) (Eq. 15.9) and the magnitude Z = √(R² + (X_L − X_C)²) (Eq. 15.11). Open access; retrieved 2026-07-29.
4. [4]OpenStax, University Physics Volume 2, §14.6 'RLC Series Circuits'. Source of the damped angular frequency ω′ = √(1/LC − (R/2L)²) (Eq. 14.46) and of the printed damping conditions — 1/LC > R²/4L² underdamped, 1/LC = R²/4L² critically damped, 1/LC < R²/4L² overdamped — which this page expresses through ζ = 1/(2Q) with the boundary at exactly ζ = 1. Open access; retrieved 2026-07-29.
5. [5]OpenStax, University Physics Volume 2, §15.4 'Power in an AC Circuit'. Source of the average power P_ave = ½I₀V₀cos φ (Eq. 15.12) and of the identification of cos φ = R/Z as the power factor — the definition that makes the −3 dB edges 'half-power' frequencies and the reason the impedance phase output matters. Open access; retrieved 2026-07-29.