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LC Resonant Frequency Calculator

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An inductor and a capacitor together have a frequency at which their opposing reactances cancel exactly. That frequency is where a radio tunes, where a filter peaks and where an oscillator settles, and it depends on nothing but the two component values. Fill in any two of inductance, capacitance and frequency and this finds the third — along with the reactance at resonance, the tank's characteristic impedance, and, if you supply the coil's resistance, the Q factor and bandwidth that decide how sharp the peak is.

Fill in two of the three and leave the one you want worked out empty.

The coil

The capacitor

Where it resonates

Ω

Mostly the coil's own winding resistance. Adds Q and bandwidth to the result.

Try:

How to use the lc resonant frequency calculator

  1. 1Fill in two of the three boxes — inductance, capacitance or frequency — and leave the third empty.
  2. 2Choose the unit beside each; microhenries and picofarads are the usual scale for radio work.
  3. 3Add the series resistance if you know it, usually the coil's own winding resistance, to get Q and bandwidth.
  4. 4Press Calculate.
  5. 5Read the missing value at the top, with the reactance and impedance figures underneath.

Examples

A medium-wave tuned circuit

Input
250 µH and 100 pF
Result
1.007 MHz — right in the middle of the AM broadcast band

A variable capacitor swinging from 40 to 400 pF is what tunes across the band.

Finding the capacitor for a target

Input
2.2 µH, tuned to 7 MHz
Result
234.8 pF

The usual design direction: the coil is what you have, and the capacitor is what you pick.

An audio-frequency tank

Input
10 mH and 1 µF
Result
1.592 kHz, reactance 100 Ω at resonance

Larger components mean lower frequencies — the relationship is an inverse square root, so a hundredfold increase in either value drops the frequency tenfold.

About the lc resonant frequency calculator

Why the square root, and what it implies

The resonant frequency is one over 2π times the square root of L times C. The square root is the part worth internalising, because it makes tuning far less sensitive than people expect. Doubling the capacitance does not halve the frequency — it divides it by the square root of two, about 1.41. To halve the frequency you need four times the capacitance, and to cover a tenfold frequency range you need a hundredfold change in one of the components.

That is why a variable capacitor for the AM broadcast band swings from around 40 pF to 400 pF: a ten-to-one capacitance range yields a bit over three-to-one in frequency, which is roughly what the band needs. It is also why tuning is usually done with the capacitor rather than the inductor — a variable capacitor is a mechanically simple thing, while a continuously variable inductor is not.

The symmetry between L and C in the formula means either can be solved for, which is what the empty box on this page does. In practice the coil is usually fixed by what is available or what fits, and the capacitor is chosen to suit — so the most-used direction is entering an inductance and a target frequency and reading off the capacitance.

Where resonance earns its keep

Radio reception is the classic case. An antenna picks up every station at once, and a tuned circuit is what selects one from the crowd — presenting a high impedance at the wanted frequency and a low one everywhere else, so only the wanted signal develops a useful voltage. The sharpness of that selection is the Q factor, and it is the difference between hearing one station and hearing three.

Oscillators use the same circuit as a frequency reference. Feed a tank a little energy each cycle to replace what resistance takes away, and it will run at its own resonant frequency indefinitely. The stability of the output depends on the Q, which is why a high-Q tank — or, where it really matters, a quartz crystal with a Q in the tens of thousands — is what sets a transmitter's frequency.

Power electronics uses resonance for a different reason: switching a transistor at the moment when the current or voltage across it passes through zero wastes almost nothing, and an LC circuit is what arranges for that moment to arrive on schedule. Induction hobs, wireless charging pads and efficient switch-mode supplies all rely on it, and the frequency they run at comes from this same formula.

Frequently asked questions

What is actually happening at resonance?
Energy is sloshing back and forth between the two components. The capacitor stores it as an electric field between its plates; the inductor stores it as a magnetic field around its winding. Each one discharges into the other, and the frequency at which that exchange happens naturally is the resonant frequency. In an ideal circuit with no resistance it would continue forever, which is exactly the behaviour an oscillator is built to exploit.
Is the frequency the same for series and parallel circuits?
The resonant frequency is, since it comes from the same formula. What differs is the behaviour there. A series LC has minimum impedance at resonance, so it draws maximum current and is used to short an unwanted frequency to ground. A parallel LC has maximum impedance, so it draws minimum current from the supply while a large current circulates internally — which is what makes it a selective filter, passing everything except the frequency it is tuned to, or vice versa depending on where it sits.
What does the Q factor tell me?
How sharp the resonance is. Q is the reactance at resonance divided by the resistance in the circuit, and the bandwidth is the resonant frequency divided by Q. A tank with a Q of 100 at 1 MHz has a 10 kHz bandwidth, which is selective enough to separate broadcast stations. A Q of 5 gives a 200 kHz bandwidth, which would receive several at once. Higher Q also means less energy lost per cycle, which is why oscillator stability depends on it.
Why does my built circuit resonate below the calculated frequency?
Stray capacitance, nearly always. Wiring, the coil's own turn-to-turn capacitance and the input capacitance of whatever the tank feeds all add to the capacitor you fitted, and since frequency falls as capacitance rises, the result lands low. A few picofarads is irrelevant at audio frequencies and decisive above a few megahertz. The usual fix is a trimmer capacitor, which is why almost every tuned radio stage has one.
Does the formula work for any inductor and capacitor?
It gives the ideal resonant frequency for any pair of values, but how closely a real circuit follows depends on the components. Inductors have winding resistance that rises with frequency, and a self-resonance of their own above which they behave capacitively. Capacitors have series inductance in their leads, with the same consequence in reverse. Both effects are negligible in the audio range and become the dominant design constraint above a few tens of megahertz.

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