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

Background.

An RLC circuit is a resistor, an inductor and a capacitor in one network, and it is the simplest circuit that can resonate. Where an RC network only smooths, an RLC network has two energy stores that can pass energy back and forth, so it rings, it has a preferred frequency, and its impedance varies sharply around that frequency instead of rolling off gently. This calculator answers the whole set of questions that follow from that in one pass: the resonant frequency, the quality factor, the bandwidth and the two half-power edges, the damping ratio and the frequency a step actually rings at, and — from the same components — the impedance magnitude, the phase, and both reactances at any frequency you name.

That last group matters enough to say plainly at the top: this page is also the RLC impedance calculator. Enter your R, L and C, set the analysis frequency, and the impedance magnitude and phase appear immediately below the resonant frequency, in either topology. There is no second page to visit.

Topology is the first choice, and it is not cosmetic. In the series arrangement all three components carry the same current; impedance is at a minimum at resonance, equal to the resistance alone, and the circuit is an acceptor — it draws maximum current at f₀. In the parallel arrangement all three see the same voltage; impedance is at a maximum at resonance, again equal to the resistance, and the circuit is a rejector. Q inverts between the two: for a given set of components, a resistance that gives a high-Q series circuit gives a low-Q parallel one, and the two Q values multiply to exactly one. That is why the topology selector changes far more than a label.

One scope limit belongs beside the answer rather than in a footnote. The parallel option models the ideal tank, with R across the inductor and capacitor. If the resistance you have in mind is the DC resistance of the coil — in series with the inductor rather than across the tank — that is a different circuit with a different resonant frequency, and this page does not model it. Fiore prints the correction, f₀ multiplied by the square root of one minus CR²/L, and the difference becomes significant below a Q of about ten. Choosing the wrong topology is the most likely way to get a wrong answer from this page.

The quality factor is the number that ties everything together. It is the ratio of resonant frequency to bandwidth, so a Q of 100 at 10 MHz means a 100 kHz-wide response. It is also one over twice the damping ratio, so it decides whether a step rings or settles. And it sets how far the impedance swings either side of resonance. A tuned radio front end wants a Q in the hundreds; a power-supply output filter wants a Q near 0.7 so that it settles without overshoot; a snubber wants a Q at or below 0.5 so that it cannot ring at all.

The half-power frequencies deserve a note because most calculators get them slightly wrong. The familiar f₀ minus half the bandwidth is an approximation valid only for high Q — Fiore prints it that way explicitly, qualified for Q of ten or more — and below a Q of 0.5 it returns a negative lower edge, which is nonsense. This page computes the exact solution instead. You can check it: the two edges here always differ by exactly f₀ divided by Q, and they always multiply to exactly f₀ squared, because resonance is the geometric mean of the two edges rather than the arithmetic one.

Everything here assumes ideal, lumped, linear components. Real inductors have winding resistance, core loss and a self-resonant frequency above which they behave as capacitors; real capacitors have equivalent series resistance and inductance; and class-2 ceramic dielectrics lose a substantial share of their marked capacitance under DC bias. Those effects move a real resonance by percent, not by parts per billion, so treat the trailing digits as arithmetic rather than as a prediction about a physical board.

What is rlc circuit calculator?

An RLC circuit contains resistance, inductance and capacitance together. It is a second-order system: two independent energy stores — magnetic field in the inductor, electric field in the capacitor — and therefore the possibility of oscillation as energy shuttles between them, with the resistance draining it. Resonance is the frequency at which the two reactances are equal in magnitude and opposite in sign, so they cancel and the network looks purely resistive. That happens at f₀ = 1/(2π√(LC)), which depends only on L and C, never on R. What R controls is the sharpness: the quality factor is (1/R)√(L/C) for the series arrangement and R√(C/L) for the parallel one, and Q equals the resonant frequency divided by the −3 dB bandwidth. In the time domain the same information appears as the damping ratio ζ = 1/(2Q). Below ζ = 1 a step response rings at a frequency slightly below f₀ and decays; at exactly ζ = 1 the circuit is critically damped and reaches its final value in the shortest time possible without overshoot; above ζ = 1 it is overdamped and simply crawls. Away from resonance the network has a complex impedance: in series form Z = R + j(X_L − X_C), whose magnitude is √(R² + (X_L − X_C)²) and whose phase is arctan((X_L − X_C)/R). Below resonance the capacitive term dominates and the circuit looks capacitive; above it, inductive. RLC networks are the tuned circuit in every radio, the LC filter on every switching regulator output, the snubber across every hard-switched device, and the tank in every oscillator.

How to use this calculator.

1. 01Choose the topology first. Series means all three components carry the same current; parallel means all three see the same voltage. Q inverts between them, so this is the choice most likely to change your answer.
2. 02If you picked parallel, check what your resistance represents. This page models the ideal tank, with R across the inductor and capacitor. Coil DC resistance sits in series with the inductor instead and is a different circuit that this page does not model.
3. 03Enter R, L and C with their units. The resonant frequency depends only on L and C; the resistance sets Q, bandwidth and damping.
4. 04Read the resonant frequency, then the impedance and phase at the analysis frequency directly below it. Set the analysis frequency to whatever your signal actually is.
5. 05Use the quality factor to judge selectivity: Q is the resonant frequency divided by the bandwidth, so a Q of 50 at 1 MHz is a 20 kHz-wide response.
6. 06Use the damping ratio to judge transient behaviour. Below 1 the circuit rings; at exactly 1 it is critically damped; above 1 it cannot oscillate. The damped ringing frequency is reported as zero at and above that boundary because there is nothing left to oscillate.
7. 07Check the sign of the phase to see which side of resonance you are on: negative means capacitive, which for a series circuit means you are below f₀.
8. 08Treat the trailing digits as arithmetic. Component tolerance, inductor core loss and ceramic DC-bias derating move a real resonance by percent.

The formula.

Resonance. Inductive reactance rises with frequency and capacitive reactance falls, so there is exactly one frequency at which they are equal. Setting 2πfL = 1/(2πfC) and solving gives f₀ = 1/(2π√(LC)) — Fiore's AC Electrical Circuit Analysis §8.2 Eq. 8.2, and OpenStax's ω₀ = 1/√(LC) at Eq. 15.17 expressed in hertz. Resistance does not appear, which is why changing R moves nothing about where the peak sits, only how sharp it is.

Quality factor. Fiore gives the series form two ways, as Eq. 8.12 Q = X₀/R_T and Eq. 8.13 Q = (1/R_T)√(L/C); the parallel form appears as Eq. 8.19 Q = R_T/X_L and Eq. 8.20 Q = R_T√(C/L). The two expressions for a given set of components are exact reciprocals, and this calculator asserts that as a test. Eq. 8.3 and 8.4 tie Q to bandwidth: BW = f₂ − f₁ and Q = f₀/BW, so BW = f₀/Q.

Half-power frequencies, and a deliberate departure from the cited source. Fiore prints f₁ ≈ f₀ − BW/2 and f₂ ≈ f₀ + BW/2 as Eq. 8.10 and 8.11, explicitly qualified as valid for higher-Q circuits, Q of about ten and above. This page computes the exact solution of the half-power condition instead: f₁ and f₂ = f₀(√(1 + 1/4Q²) ∓ 1/2Q). The two agree to better than 0.2 % at Q = 10 and diverge sharply below Q ≈ 3; below Q = 0.5 the approximation returns a negative lower edge. The exact form satisfies two identities the approximation does not — the edges differ by exactly f₀/Q, and their product is exactly f₀² — and both are asserted in the test suite. The approximation is not wrong, it is out of its stated range, and the substitution is recorded here rather than made silently.

Damping. OpenStax §14.6 gives the damped angular frequency as Eq. 14.46, ω′ = √(1/LC − (R/2L)²), with the printed conditions 1/LC > R²/4L² for underdamped, equality for critically damped and the reverse inequality for overdamped. Writing ζ = 1/(2Q) turns that into ω′ = ω₀√(1 − ζ²) with the boundary at exactly ζ = 1, which is the form used here because it puts the classification on a single dimensionless scalar. The damped frequency is reported as zero at and beyond ζ = 1: the square root would be imaginary, and physically there is no oscillation to have a frequency.

Impedance. OpenStax §15.3 gives X_L = ωL at Eq. 15.8 and X_C = 1/(ωC) at Eq. 15.3, the series magnitude Z = √(R² + (X_L − X_C)²) at Eq. 15.11 and the phase φ = tan⁻¹((X_L − X_C)/R) at Eq. 15.9. For the parallel tank the same algebra runs on admittance instead: Y = 1/R + j(ωC − 1/(ωL)), the impedance magnitude is the reciprocal of |Y|, and the phase is the negative of arctan(R times the susceptance). At resonance the reactive term vanishes in both cases, so |Z| = R and the phase is exactly zero — the calculator is asserted against that in both topologies.

Rounding stage. Every quantity is carried at full decimal precision and rounded once, at the return boundary, to ten decimal places. The damping verdict classifies the unrounded damping ratio, not the displayed one, so a circuit that is a hair over ζ = 1 is called overdamped even when the displayed ratio reads 1.0000000000.

What the model leaves out. Winding resistance and core loss in the inductor; equivalent series resistance and inductance in the capacitor; the inductor's own self-resonant frequency, above which it behaves capacitively and none of this applies; skin and proximity effect; dielectric loss; and DC-bias derating in class-2 ceramics, which can remove more than half of a marked value. For the parallel topology it also assumes R is across the tank rather than in series with the coil — the case Fiore's Eq. 8.21 covers and this page does not.

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.