LC Resonant Frequency Calculator
Find the resonant frequency of an LC tank circuit from its inductance and capacitance.
How it works
f₀ = 1 ÷ (2π·√(L·C))
An inductor and capacitor together form a tank circuit that naturally oscillates at one frequency, exchanging energy between the magnetic field of the coil and the electric field of the capacitor. That resonant frequency is f₀ = 1/(2π√(LC)) — it depends only on the product L·C, so halving one and doubling the other leaves it unchanged. Radios tune stations by varying C to move f₀ onto the broadcast frequency.
Worked example
For L = 1 mH (0.001 H) and C = 100 nF (1×10⁻⁷ F): √(LC) = √(10⁻³ × 10⁻⁷) = √(10⁻¹⁰) = 10⁻⁵. f₀ = 1/(2π × 10⁻⁵) ≈ 15,915 Hz ≈ 15.9 kHz.
Sources: LC circuit — Wikipedia
Frequently asked questions
Does resistance change the resonant frequency?
In the ideal formula, no — resonance depends only on L and C. Real resistance slightly shifts and broadens the peak, but f₀ = 1/(2π√(LC)) is the standard design value.
Why does only the product L·C matter?
The formula contains L and C only as their product under the square root, so many L/C combinations give the same frequency. Designers pick the pair that also suits the desired impedance and current.
What is angular frequency?
Angular frequency ω = 2πf measures oscillation in radians per second. At resonance ω₀ = 1/√(LC), which is often more convenient in circuit equations.
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This calculator is for educational purposes. Double-check important results before acting on them.