What this calculator does
An inductor and a capacitor together form a circuit that prefers one particular frequency. At resonance their opposing reactances cancel exactly, leaving only the resistance, and the circuit responds far more strongly there than anywhere else.
That selectivity is what makes radio possible. Tuning a receiver means changing one of the two components so the resonant frequency lands on the station you want and rejects everything else.
The formula
The resonant frequency is one divided by 2π times the square root of inductance times capacitance. The Q factor is one over the resistance times the square root of L over C, and the bandwidth is the resonant frequency divided by Q.
| Term | Meaning |
|---|---|
| Resonance | The frequency at which inductive and capacitive reactance are equal and cancel each other out. |
| Q factor | How sharply tuned the circuit is. High Q means a narrow, selective response; low Q means a broad one. |
| Bandwidth | The width of the frequency band the circuit responds strongly to, measured between the points 3 dB below the peak. |
The inputs explained
| Field | What to enter |
|---|---|
| Inductance (H) | Inductance in henries. A 1 millihenry coil is entered as 0.001. |
| Capacitance (F) | Capacitance in farads. A 1 microfarad capacitor is 0.000001. |
| Series resistance (Ω) | Series resistance in ohms, which determines the Q factor and bandwidth but not the resonant frequency. |
When to use it
Tuning a radio stage
The resonant frequency has to match the station, and the Q factor determines how well neighbouring stations are rejected.
Designing a filter
An LC pair forms a band-pass or band-stop filter, and the same two numbers describe where it acts and how sharply.
Diagnosing unwanted resonance
Stray inductance and capacitance can resonate where they are not wanted, and knowing the frequency is the first step in suppressing it.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does capacitance shift the resonant frequency?
A fixed inductor paired with a range of capacitors.
| Capacitance | Resonant frequency | Q factor |
|---|---|---|
| 1 µF | 5,032.92 Hz | 3.162 |
| 0.09999999999999999 µF | 15,915.49 Hz | 10.000 |
| 0.01 µF | 50,329.21 Hz | 31.623 |
Questions
Why does resistance not affect the resonant frequency?
Because resonance occurs where inductive and capacitive reactance cancel, and resistance is not a reactance. It damps the response and broadens the peak without moving where that peak sits.
What does a high Q factor mean in practice?
A sharp, narrow response with a large voltage build-up at resonance. Good for selectivity, but it also means the circuit rings for longer after a disturbance.
Is series resonance the same as parallel?
The frequency formula is the same, but the behaviour is opposite. A series circuit has minimum impedance at resonance and draws maximum current; a parallel circuit has maximum impedance and draws minimum current.
Why does the voltage across the components exceed the supply?
Because at resonance the inductor and capacitor voltages are large and opposite, cancelling each other in the total while each individually can far exceed the source. This is real and can damage components rated only for the supply voltage.
For a simpler single-pole filter, see the low pass filter calculator. For the impedance of the components at any frequency, see the impedance calculator.