Calculators
LC Resonance Calculator
Calculate LC resonant frequency and reactance from inductance and capacitance.
LC Resonance Calculator tool
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About This Tool
An inductor and capacitor can form a tuned LC circuit whose natural frequency is determined by their component values. This calculator rearranges the ideal resonance relationship f₀ = 1/(2π√LC) to solve for resonant frequency, inductance, or capacitance with common engineering units. Frequency results also report angular frequency and the reactance magnitude shared by the inductor and capacitor at resonance. This makes it useful for checking tank circuits, tuned filters, oscillators, radio-frequency exercises, and electronics experiments without an API or uploaded data.
How To Use It
- Choose whether to solve for resonant frequency, inductance, or capacitance.
- Enter the two known values and select their engineering units.
- Choose the desired result unit when solving for a component value. Frequency mode also shows angular frequency and the equal inductive/capacitive reactance magnitude.
- Treat the result as an ideal starting point and account for component tolerance, losses, loading, and parasitic effects in a physical circuit.
Examples
100 µH with 100 pF
The ideal resonant frequency is about 1.59155 MHz. At resonance, the inductor and capacitor each have a reactance magnitude of about 1000 Ω.
1 mH with 1 µF
The ideal resonant frequency is about 5.033 kHz. Increasing either L or C lowers resonance because frequency varies inversely with the square root of LC.
Tuning comparison
If capacitance is increased by a factor of four while inductance stays fixed, the ideal resonant frequency is halved. This square-root relationship is useful when estimating how component changes move a tuned circuit.
Choose a capacitor for a target frequency
With a 100 µH inductor and a target of about 1.59155 MHz, rearranging the resonance formula gives approximately 100 pF.
Useful Notes
Resonant frequency formula
For an ideal LC circuit, f₀ = 1/(2π√LC), with L in henries and C in farads. The equivalent angular frequency is ω₀ = 1/√LC = 2πf₀.
Why resonance occurs
Inductive reactance XL = 2πfL rises with frequency, while capacitive reactance XC = 1/(2πfC) falls. At ideal resonance their magnitudes are equal. Solving XL = XC gives the standard LC resonance equation.
Characteristic impedance
At ideal resonance, the magnitude of each component's reactance equals √(L/C). This value is often called the characteristic impedance of the ideal LC tank and provides a useful impedance scale for the network.
Series versus parallel LC
The same ideal L and C values give the same resonance frequency in simple series and parallel LC networks, but their impedance behavior differs. An ideal series LC tends toward minimum impedance at resonance, while an ideal parallel tank tends toward maximum impedance.
Real component limitations
Physical inductors have winding resistance, parasitic capacitance, finite Q, and a self-resonant frequency. Capacitors have ESR, ESL, leakage, and tolerance. Source and load impedances also affect a real response, so measured resonance and bandwidth can differ from the ideal calculation.
Choosing practical components
Check component datasheets and tolerances when a precise resonant frequency matters. The ideal formula is a strong first calculation, but high-frequency layouts may require accounting for PCB traces, device input capacitance, probe loading, and other parasitic elements.
FAQ
What units should I use for L and C?
You can use the unit selectors. The calculator converts the selected inductance to henries and capacitance to farads before applying the formula.
Can I solve for the capacitor or inductor value?
Yes. Choose Inductance or Capacitance under Solve for, then enter the target resonant frequency and the other component value. The calculator rearranges the same ideal LC resonance equation.
Does resistance change this calculated LC frequency?
This tool calculates ideal lossless LC resonance. Resistance and loading determine damping, Q, bandwidth, and can shift practical measured behavior, so they must be considered for a real circuit.
Are inductive and capacitive reactance equal at resonance?
Their magnitudes are equal in the ideal LC model. XL is positive reactance and XC is negative reactance, so their reactive effects cancel in an ideal series combination.
Why does a larger capacitor lower resonant frequency?
Frequency is proportional to 1/√C when inductance is fixed. A larger capacitance therefore increases the LC energy-exchange timescale and lowers the natural frequency.