LC Resonant Frequency Calculator
From an inductance and a capacitance, get the frequency at which the coil and capacitor exchange energy most efficiently — the number behind every radio dial, filter, and oscillator.
Two inputs, one answer
Enter the inductance and capacitance and the calculator returns the resonant frequency 1 ÷ (2π√(L × C)) at once.
Use SI units
Enter the inductance in henries (H) and the capacitance in farads (F) — then the frequency comes back in hertz (Hz).
What is an LC circuit's resonant frequency?
Inductance and capacitance in, frequency out
An LC circuit pairs an inductor (L) with a capacitor (C), and energy sloshes back and forth between the coil's magnetic field and the capacitor's electric field. It does this fastest at one special frequency — the resonant frequency — given by f = 1 ÷ (2π√(L × C)). At that frequency the inductor and capacitor exchange energy most efficiently, so a circuit tuned there responds far more strongly than at any other frequency. Increasing either L or C lowers the resonant frequency, because both sit under the square root. This single number is what radios, filters, and oscillators are set to.
Enter the inductance and capacitance to get the resonant frequency instantly.
One short formula, built from the inductance (L) and the capacitance (C).
f = 1 ÷ (2π√(L × C))The frequency is the reciprocal of two pi times the square root of the product of the inductance and the capacitance. Because L and C are multiplied under the square root, what matters is the product L × C: any pair with the same product gives the same resonant frequency. Larger L or C means a larger product, which means a lower frequency.
Suppose a coil has L = 1 mH = 0.001 H and a capacitor has C = 1 µF = 0.000001 F.
Multiply L and C
0.001 × 0.000001 = 0.000000001 — the product under the square root.
Apply the formula
1 ÷ (2 × π × √0.000000001) = 5032.92 Hz — about 5.03 kHz.
Cross-check
Quadruple the capacitance to 4 µF and the frequency halves to about 2516.46 Hz — frequency scales with the inverse square root of L × C.
The resonant frequency tells you where the LC circuit "wants" to oscillate — the frequency at which the inductor and capacitor pass energy back and forth most efficiently, with very little wasted. For the worked example, about 5.03 kHz is the tone the circuit naturally rings at. The key insight is the inverse-square-root relationship: the frequency depends on the square root of the product L × C, not on L or C alone, so increasing either component lowers the frequency, and you must quadruple L × C to halve the frequency. This is exactly how tuning works in practice: a radio picks a station, and a filter or oscillator picks a tone, by choosing L and C so the circuit resonates at the frequency you want. A bigger coil or a bigger capacitor tunes the circuit lower; smaller ones tune it higher. Because only the product matters, you can trade a larger inductor for a smaller capacitor and keep the same frequency.
The formula is exact for an ideal lossless LC circuit, but a couple of practical points are worth keeping in mind.
Ideal components and SI units
This tool assumes an ideal LC circuit with no resistance. Real coils and capacitors have some resistance and losses, which shift the peak slightly and broaden the resonance (a lower quality factor, or Q), and component values carry tolerances. For most design and learning purposes the ideal formula is an excellent first estimate; precise work then accounts for resistance and parasitic effects. Enter the inductance in henries and the capacitance in farads so the frequency comes back in hertz — convert mH, µH, µF, nF, and pF to H and F first.