LC Resonance Calculator
Use this tool to calculate resonance frequency, inductance, or capacitance for an ideal LC tank circuit.
Tip: For practical circuits with resistance, real resonance can shift slightly from this ideal value.
What Is LC Resonance?
An LC circuit contains an inductor (L) and a capacitor (C). At a specific frequency, called the resonant frequency, the energy swaps back and forth between the magnetic field of the inductor and the electric field of the capacitor. At this point, the inductive reactance and capacitive reactance are equal in magnitude, producing resonance.
Designers use LC resonance in radio tuning, filters, oscillators, impedance matching networks, and sensor electronics. If you have ever tuned a station on a traditional radio, you have used a resonant LC circuit in practice.
LC Resonance Formula
Primary Equation
The ideal resonant frequency for an LC circuit is:
- f₀ = 1 / (2π√(LC))
Where:
- f₀ is the resonant frequency in hertz (Hz)
- L is inductance in henries (H)
- C is capacitance in farads (F)
Rearranged Forms
You can solve the same relationship for unknown inductance or capacitance:
- L = 1 / ((2πf₀)²C)
- C = 1 / ((2πf₀)²L)
How to Use This Calculator
Step-by-step
- Select a calculation mode: frequency, inductance, or capacitance.
- Enter the known values using the correct units (such as μH, nF, kHz).
- Click Calculate.
- Review the result plus supplemental values like angular frequency, period, and reactance at resonance.
The tool automatically converts units in the background, so you can mix practical component units like μH and nF without manual conversions.
Example Use Cases
Example 1: Find Resonant Frequency
Given L = 10 μH and C = 100 nF, the resonant frequency is roughly 159.15 kHz. This is a common range for switching and filtering experiments.
Example 2: Pick an Inductor for a Target Frequency
If you need 1 MHz resonance with a 220 pF capacitor, solve for L. The result tells you the ideal inductor value before accounting for real-world tolerances and parasitics.
Example 3: Determine Required Capacitance
If your inductor is fixed at 47 μH and you want a resonant point near 455 kHz (classic IF frequency), solve for C to choose a capacitor close to that value.
Practical Engineering Notes
- Real inductors include winding resistance and parasitic capacitance.
- Real capacitors include ESR (equivalent series resistance) and tolerance drift.
- Temperature affects both L and C, so resonance can shift with environment.
- At high frequencies, PCB trace inductance/capacitance becomes significant.
- For narrowband designs, always verify with simulation and measurement.
Common Mistakes
1) Unit mismatch
Mixing μH with H or nF with F without conversion can cause errors by factors of thousands or millions.
2) Forgetting ideal assumptions
The ideal equation assumes no resistance and no loss. Real circuits have damping, lowering Q and shifting peak response.
3) Ignoring tolerance stack-up
A ±10% inductor and ±5% capacitor can create meaningful spread in final resonant frequency. Always budget for component tolerance in design margins.
Final Thoughts
An LC resonance calculator is one of the fastest ways to move from concept to component selection in analog and RF work. Start with the ideal value, then refine through simulation, prototype testing, and measured tuning. Used this way, a simple formula becomes a powerful design workflow.