LC Filter Calculator — Resonant Frequency, Impedance & Wavelength
Enter inductance (L) and capacitance (C) in any SI prefix unit to find the resonant frequency, characteristic impedance, and reactance of an LC filter or tank circuit.
Frequency where XL = XC — inductive and capacitive reactance cancel
- 1
L × C product
0.0001 × 0 = 0 - 2
√(L × C)
√(0) = 0 - 3
2π × √(LC)
2π × 0 = 0.000001 - 4
Resonant frequency f₀ = 1 ÷ (2π × √(LC))
1 ÷ (2π × 0) = 1.5915 MHzThe frequency at which inductive and capacitive reactances exactly cancel.
How does this calculator work?
An LC circuit resonates at f₀ = 1/(2π√(LC)), where inductive and capacitive reactances cancel. Characteristic impedance Z₀ = √(L/C) equals both reactances at f₀. Use L in H and C in F — the calculator accepts SI prefix units (μH, pF, etc.) and also shows angular frequency ω₀ and free-space wavelength λ.
Formula
How this is calculated
An LC circuit consists of an inductor (L) and a capacitor (C). At the resonant frequency f₀, the inductive reactance XL = 2πf₀L and capacitive reactance XC = 1/(2πf₀C) are equal and opposite, so they cancel. This makes the ideal LC circuit oscillate indefinitely at f₀ = 1/(2π√(LC)) — the stored energy cycles between the magnetic field in the inductor and the electric field in the capacitor.
The characteristic impedance Z₀ = √(L/C) sets the natural impedance of the circuit. It equals the common value of XL and XC at resonance and is important for matching the LC filter to source and load impedances. In a matched bandpass filter stage, source and load are both terminated at Z₀ to maximise power transfer. The angular frequency ω₀ = 2πf₀ appears naturally in most AC circuit equations. The wavelength λ = c/f₀ shows the free-space electromagnetic wavelength corresponding to f₀ — relevant when using LC tanks as antenna matching networks.
This calculator assumes ideal lossless components. Real inductors have series resistance (which limits Q and broadens the resonance) and real capacitors have leakage and equivalent series resistance (ESR). For a circuit with explicit series resistance R, use the RLC resonant frequency calculator and check the quality factor Q.
Frequently asked questions
f₀ = 1 / (2π√(LC)). At this frequency inductive reactance XL = 2πf₀L equals capacitive reactance XC = 1/(2πf₀C), so they cancel, and the circuit exhibits pure resonance — maximum current in a series circuit or maximum impedance in a parallel circuit.
Z₀ is the impedance seen at the ports of an LC ladder when terminated correctly, and also the common value of XL and XC at resonance. Matching source and load to Z₀ gives maximum power transfer. For a 100 μH / 100 pF circuit Z₀ = √(10⁻⁴/10⁻¹⁰) = 1 kΩ.
Choose a desired f₀ and a characteristic impedance Z₀ that matches your circuit. Then L = Z₀/(2πf₀) and C = 1/(2πf₀Z₀). For example, for f₀ = 1 MHz and Z₀ = 50 Ω: L = 50/(2π×10⁶) ≈ 7.96 μH and C = 1/(2π×10⁶×50) ≈ 3.18 nF.
Also known as
TG we-Calculate Editorial Team. (2026). LC Filter Calculator — Resonant Frequency, Impedance & Wavelength [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/lc-filter-calculator
TG we-Calculate Editorial Team. "LC Filter Calculator — Resonant Frequency, Impedance & Wavelength." TG we-Calculate. 2026. https://we-calculate.com/calculator/lc-filter-calculator.
TG we-Calculate Editorial Team, "LC Filter Calculator — Resonant Frequency, Impedance & Wavelength," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/lc-filter-calculator
@misc{wecalculate_lc_filter_calculator, title = {LC Filter Calculator — Resonant Frequency, Impedance & Wavelength}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/lc-filter-calculator}}, year = {2026}, note = {TG we-Calculate} }
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