LC Resonance & Reactance Calculator
Resonant frequency, reactance, impedance and Q for an LC circuit.
How it works
An inductor's reactance rises with frequency and a capacitor's falls. Where they cross, they are equal and opposite, cancel exactly, and the circuit resonates:
f₀ = 1 ÷ (2π√(LC))
XL = 2πfL, XC = 1 ÷ (2πfC)
The square root has a practical consequence people forget: to halve the resonant frequency you must quadruple L or C. Tuning across a 2:1 frequency range needs a 4:1 capacitor swing, which is why variable capacitors in radios are physically large and why band-switching exists at all.
At resonance a series LC looks like a short circuit — only the resistance is left — while a parallel LC looks like an open circuit. Same components, opposite behaviour, and which one you have determines whether the circuit passes or blocks its resonant frequency. That is the difference between a notch filter and a bandpass.
Q is the sharpness of it, and for a series circuit it is (1/R)√(L/C). Everything that matters follows: bandwidth is f₀ ÷ Q, so a high-Q circuit is narrow and selective and a low-Q one is broad and gentle. In a tuned radio front end you want Q in the hundreds. In a power supply filter you want it low, because a high-Q LC across a switching supply rings, and ringing on a power rail is how a design that worked on the bench fails EMC.
Resistance is what kills Q, and most of it is in the inductor. Capacitors are close to ideal; coils have wire resistance, core losses, and skin effect that gets worse the higher you go.
Common questions
Series or parallel?
At resonance, a series LC is a short circuit and a parallel LC is an open circuit. Series across a signal path notches out that frequency; parallel in the path passes it. Getting them the wrong way round gives you exactly the opposite filter.
Why is my measured frequency lower than calculated?
Stray capacitance, almost always. Wiring, the coil's own turn-to-turn capacitance and the input capacitance of whatever you connected all add to C. At high frequencies a few picofarads of layout shifts things noticeably.
What Q should I aim for?
High — 50 to several hundred — for a selective tuned circuit. Low, under 1 if you can, for a power supply filter, because a high-Q LC rings on every load step. Adding deliberate series resistance to damp it is a normal and correct thing to do.
Does the capacitor type matter?
Considerably, above audio. Class 2 ceramics like X7R lose a large fraction of their capacitance under DC bias and drift with temperature, so a tuned circuit built with them will not sit where you calculated. Use C0G/NP0 for anything that has to stay put.