LC Resonant Frequency Calculator
Inductance Unit
Capacitance Unit
Resonant Frequency1.5915 MHz
Angular Frequency (ω)10,000,000.00 rad/s
Period0.6283 µs
An inductor and capacitor placed together form a resonant tank circuit that naturally oscillates at one frequency where their reactances cancel. This calculator finds that resonant frequency from the inductance and capacitance you supply, and also reports the angular frequency and the oscillation period. Engineers use it to tune radio receivers, design oscillators, set filter corner frequencies, and build impedance-matching networks.
Formula
f = 1 / (2π · √(L · C))
- f
- Resonant frequency (hertz)
- L
- Inductance (henries)
- C
- Capacitance (farads)
- π
- Pi, approximately 3.14159
How it works
- Enter the inductance with its unit (H, mH, µH, or nH) and the capacitance with its unit (F down to pF); both are converted to base SI units.
- The calculator evaluates f = 1 / (2π·√(L·C)) to find the resonant frequency in hertz, scaling the display to kHz or MHz where helpful.
- It also derives the angular frequency ω = 2π·f in radians per second and the period in microseconds.
Worked example
A tuned circuit uses a 100 µH inductor and a 100 pF capacitor.
- Convert units: L = 0.0001 H, C = 1e-10 F.
- L·C = 0.0001 × 1e-10 = 1e-14.
- √(L·C) = 1e-7; 2π·√(L·C) = 6.2832e-7.
- f = 1 / 6.2832e-7 ≈ 1,591,549 Hz.
The circuit resonates at about 1.5915 MHz.
Frequently asked questions
- What happens at the resonant frequency?
- At resonance the inductive reactance equals the capacitive reactance and they cancel, so a series LC circuit shows minimum impedance while a parallel LC tank shows maximum impedance. Energy sloshes back and forth between the magnetic and electric fields.
- How do I shift the resonant frequency up?
- Because frequency is inversely proportional to the square root of L·C, decreasing either the inductance or the capacitance raises the resonant frequency. Halving the product L·C raises the frequency by roughly 41%.
- Does this formula apply to both series and parallel LC circuits?
- Yes, the ideal resonant frequency f = 1/(2π√(LC)) is identical for both topologies. They differ in their impedance behaviour at resonance, not in the resonant frequency itself.
- Why is resistance not part of the formula?
- The ideal resonant frequency depends only on L and C. Resistance affects the quality factor and bandwidth of the resonance and slightly shifts the peak in damped circuits, but it is omitted from this first-order calculation.