Resonant Frequency Calculator
Find the resonant frequency of an LC circuit. Enter the inductance (H, mH, µH or nH) and the capacitance (F, µF, nF or pF) to get the resonant frequency, the angular frequency, and the period of oscillation.
Example: with Inductance 100 · Inductance unit µH · Capacitance 100 · Capacitance unit pF → Resonant frequency: 1.5915 MHz (1,591,549 Hz).
- Angular frequency ω10.0000 Mrad/s
- Period T628.3185 ns
Computed by the calculator below using its default values. Change any input to see your own numbers.
At resonance the inductive and capacitive reactances cancel, leaving f = 1/(2π√(LC)). Larger L or C lowers the frequency; the two trade off through their product.
Where the reactances cancel
An inductor and a capacitor push back on alternating current in opposite ways: inductive reactance rises with frequency while capacitive reactance falls. At one special frequency the two are equal and cancel, and the circuit swaps energy freely between the magnetic field of the coil and the electric field of the capacitor. That is resonance, and it lands at f = 1/(2π√(LC)).
Only the product LC sets the frequency, so you can trade a big inductor for a small capacitor and land on the same station. That trade-off is the basis of radio tuning, oscillators, and the traps in antennas. Doubling either L or C does not halve the frequency — because of the square root, it drops it by a factor of √2.
How it’s calculated
Resonant frequency f = 1/(2π√(LC)) with L in henries and C in farads. Inputs convert with µH = 1e-6 H, mH = 1e-3 H, nH = 1e-9 H, pF = 1e-12 F, nF = 1e-9 F, µF = 1e-6 F. Angular frequency ω = 2πf and period T = 1/f follow directly.
An ideal, lossless series or parallel LC circuit. Real components have resistance and parasitics that shift and broaden the resonance slightly.
Resonant frequency for LC pairs
| Inductance | Capacitance | Resonant frequency |
|---|---|---|
| 100 µH | 100 pF | 1.5915 MHz |
| 10 µH | 10 pF | 15.915 MHz |
| 1 mH | 1 µF | 5.033 kHz |
| 100 mH | 10 µF | 159.15 Hz |
Computed with f = 1/(2π√(LC)); rounded.
Common mistakes
- Forgetting to convert prefixes — µH and pF are 10⁻⁶ and 10⁻¹² of the base units.
- Dropping the 2π, which gives the angular frequency ω instead of the frequency f.
- Expecting frequency to halve when L or C doubles; the square root makes it fall by √2.
- Confusing series and parallel LC — both share this resonant frequency, but their impedance behavior is opposite.
Frequently asked questions
What is the LC resonant frequency formula?
f = 1/(2π√(LC)), with inductance L in henries and capacitance C in farads. The result is in hertz.
What happens at the resonant frequency?
The inductive and capacitive reactances are equal and cancel. Energy sloshes between the coil and the capacitor, and the circuit responds most strongly at that frequency.
How do L and C affect the frequency?
Only their product matters. Increasing either L or C lowers the resonant frequency, and because of the square root, quadrupling the product halves the frequency.
Is the formula the same for series and parallel LC?
Yes, the resonant frequency f = 1/(2π√(LC)) is identical. What differs is that a series circuit has minimum impedance at resonance while a parallel circuit has maximum impedance.