Resonant Frequency Calculator (LC Circuit)
Find the resonant frequency of an LC circuit from its inductance and capacitance. Enter the values in the everyday units of microhenries and nanofarads and get the frequency in Hz plus a scaled kHz or MHz reading.
Enter Values
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How to use this calculator
- Enter the inductance L in microhenries (µH).
- Enter the capacitance C in nanofarads (nF).
- Read the resonant frequency in Hz and in a friendly kHz/MHz unit, plus the angular frequency ω₀.
How it works
An inductor and capacitor exchange energy back and forth, and the exchange is fastest at the resonant frequency f₀ = 1 / (2π√(L·C)). The formula needs L in henries and C in farads, so the tool first converts your microhenries (×1e-6) and nanofarads (×1e-9). It then reports f₀ in hertz, rescales it to kHz or MHz, and gives the angular frequency ω₀ = 2π·f₀ in radians per second.
Worked example
Worked example. For L = 100 µH and C = 100 nF: L·C = 1e-4 × 1e-7 = 1e-11, √(L·C) = 3.1623e-6, so f₀ = 1 / (2π × 3.1623e-6) ≈ 50,329.21 Hz ≈ 50.329 kHz.
Common mistakes
- Entering L in henries or C in farads — the boxes expect microhenries and nanofarads.
- Mixing up nanofarads and microfarads: 1 µF = 1000 nF, a factor of a thousand that shifts the frequency ~31×.
- Expecting this ideal result to include damping — real circuits have resistance and a finite Q that broadens the peak.
Frequently asked questions
Does the formula differ for series and parallel LC?
No. Both an ideal series and an ideal parallel LC circuit resonate at f₀ = 1 / (2π√(L·C)); what differs is the impedance behaviour (minimum for series, maximum for parallel) at that frequency.
How do I enter a capacitor rated in microfarads?
Multiply by 1000 to convert to nanofarads first — e.g. 0.1 µF is 100 nF.
What is the angular frequency for?
ω₀ = 2π·f₀ is the same resonance expressed in radians per second, which is the form used directly in reactance formulas such as XL = ωL and XC = 1/(ωC).
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