LC Resonance Frequency Calculator
An inductor and capacitor connected together form a resonant circuit that oscillates strongly at one particular frequency. That frequency, given by the Thomson formula, is the foundation of radio tuning, oscillators, and filters. Enter the inductance and capacitance using convenient component units (microhenries and picofarads), and this calculator returns the resonant frequency in hertz, kilohertz, and megahertz, plus the angular frequency in radians per second. The formula is exact physics, so the result needs no empirical assumption beyond the component values you supply.
Resonance frequency formula
L (henries) = L_uH * 1e-6
C (farads) = C_pF * 1e-12
f = 1 / (2 * pi * sqrt(L * C))
omega = 2 * pi * f
kHz = f / 1,000, MHz = f / 1,000,000
This is the Thomson resonance formula for an ideal LC circuit. Inductance and capacitance enter symmetrically under the square root, so doubling either one reduces the frequency by the same factor of root two.
Notes on resonant circuits
- The constant pi is a mathematical constant, approximately 3.14159; no empirical figure is assumed.
- Resistance sets the Q factor and bandwidth but not the ideal resonant frequency.
- Real inductors have parasitic capacitance and resistance that shift the actual resonance slightly.
- One microhenry is 1e-6 henry; one picofarad is 1e-12 farad, per SI prefixes.
- To raise the frequency, decrease L or C; to lower it, increase either.
Resonance frequency: frequently asked questions
What is the resonant frequency of an LC circuit?
It is the frequency at which the inductive reactance equals the capacitive reactance, so the circuit oscillates most readily. The Thomson formula gives it as f = 1 / (2 pi times the square root of L times C), where L is inductance in henries and C is capacitance in farads.
What units should I use?
Enter inductance in henries and capacitance in farads. Because real components are usually in microhenries and picofarads, this calculator lets you enter those directly and converts internally: 1 microhenry is 1e-6 H and 1 picofarad is 1e-12 F.
Does resistance affect resonant frequency?
In an ideal series or parallel LC circuit, resistance does not change the resonant frequency given by the Thomson formula; it affects the sharpness, or Q factor, of the resonance. This calculator gives the undamped resonant frequency, which is the standard reference value.
What is angular frequency?
Angular frequency, omega, equals 2 pi times the frequency in hertz, expressed in radians per second. For an LC circuit omega equals 1 divided by the square root of L times C. The calculator reports both ordinary frequency and angular frequency.
Where is this formula used?
Tuned LC circuits set the operating frequency of radios, oscillators, filters, and wireless transmitters. Choosing L and C to hit a target frequency is a routine design task, and this formula is the starting point taught in every electronics course.
Official sources
- National Institute of Standards and Technology: International System of Units (SI).
- NASA Glenn Research Center: oscillation and frequency fundamentals.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.