LC Resonant Frequency Calculator
Calculate the resonant frequency of an LC circuit (tank circuit). Enter inductance (mH) and capacitance (µF) to find frequency and characteristic impedance.
How to use this tool
- Enter inductance (l) and capacitance (c) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your resonant frequency and the full breakdown beneath it.
An LC circuit resonates when energy oscillates between the inductor (L) and capacitor (C). The resonant frequency is f = 1 / (2π√(LC)). At resonance the inductive and capacitive reactances are equal and cancel, leaving only the circuit's resistance. The characteristic impedance is Z₀ = √(L/C).
Formula
Resonant Frequency: f = 1 / (2π √(L × C))
Angular Frequency: ω = 2πf
Characteristic Impedance: Z0 = √(L / C)
Where L is in henries (input in mH ÷ 1000) and C is in farads (input in µF ÷ 106).
How it works
An LC circuit resonates when inductive reactance equals capacitive reactance. At this frequency energy oscillates between the magnetic field of the inductor and the electric field of the capacitor with minimum impedance (series resonance) or maximum impedance (parallel resonance).
The characteristic impedance Z0 describes the impedance of the circuit at resonance and is useful for matching LC tanks to transmission lines. Inputs are entered in millihenries and microfarads and converted internally to SI base units before calculation.
Worked example
Worked example — 10 mH and 10 µF
- Inputs: L = 10 mH = 0.01 H, C = 10 µF = 10 × 10−6 F.
- Product L × C = 0.01 × 10−5 = 10−7.
- √(L × C) = √(10−7) ≈ 3.1623 × 10−4.
- f = 1 / (2π × 3.1623 × 10−4) ≈ 503.29 Hz.
Resonant Frequency: 503.29 Hz
Key terms
- Resonant Frequency
- The frequency at which the inductive and capacitive reactances of an LC circuit are equal and cancel out, resulting in maximum energy transfer or oscillation.
- Angular Frequency (ω)
- Resonant frequency expressed in radians per second: ω = 2πf. Used in phasor analysis and differential equations describing LC circuits.
- Characteristic Impedance (Z0)
- Equal to √(L/C); characterises the impedance magnitude of the LC tank at resonance, useful for filter and impedance-matching design.
- Tank Circuit
- Another name for a parallel LC circuit, which presents very high impedance at resonance and is used in oscillators and RF filters.
- Quality Factor (Q)
- A measure of how selective (narrow-bandwidth) an LC circuit is. Not calculated here — Q depends on the series resistance and equals ωL/R or 1/(ωCR).
Frequently asked questions
- What is a tank circuit?
- A parallel LC circuit used to select or generate a specific frequency, common in radio transmitters and AM/FM receivers.
- How do I convert µH to mH?
- Divide by 1000. For example, 100 µH = 0.1 mH. Enter 0.1 in the inductance field.