LC Resonance Calculator
Calculate the ideal resonant frequency and angular frequency of an LC tank circuit from inductance and capacitance.
Reverse modes solve the inductance or capacitance required for a target frequency, supporting component selection for RF circuits, oscillators, filters, and impedance-matching networks.
Results use ideal lumped components. Verify tolerance, Q factor, self-resonant frequency, parasitic resistance, layout, and loading before finalizing a hardware design.
Engineering tool
LC Resonance Calculator
Calculate resonant frequency from L and C, or solve the required inductance or capacitance for a target frequency.
Inductor value in the ideal LC tank circuit.
Capacitor value in the ideal LC tank circuit.
Resonant frequency (f₀)
159.154943 kHz
f₀ = 1 / (2π√(LC))
Result console
- Resonant frequency (f₀)
- 159.154943kHz
- Angular frequency (ω₀)
- 1,000,000rad/s
- Inductance (L)
- 10µH
- Capacitance (C)
- 100nF
LC Tank Circuit Diagram
In this parallel tank, the inductor and capacitor exchange stored energy at the circuit's natural resonant frequency.
Formula reference
LC Resonance Formulas
Use SI base units inside each equation. The reverse forms select an ideal L or C for a known target frequency and the other component value.
Resonant frequency: f₀ = 1 / (2π√(LC))Angular frequency: ω₀ = 2πf₀Required inductance: L = 1 / ((2πf₀)²C)Required capacitance: C = 1 / ((2πf₀)²L)Variable definitions
- f₀
- Resonant frequency in hertz (Hz)
- ω₀
- Angular resonant frequency in radians per second (rad/s)
- L
- Inductance in henries (H)
- C
- Capacitance in farads (F)
How to Use This Calculator
- Select whether to calculate frequency, inductance, or capacitance.
- Enter the two known quantities and select their engineering units.
- Select Calculate to apply the ideal LC resonance equation.
- Compare the normalized L, C, f₀, and ω₀ values in the result card.
Worked Example
10 µH and 100 nF LC Tank
L = 10 µH = 10 × 10⁻⁶ H
C = 100 nF = 100 × 10⁻⁹ F
√(LC) = √(10 × 10⁻⁶ × 100 × 10⁻⁹) = 1 µs
f₀ = 1 / (2π × 1 µs)
f₀ ≈ 159.15 kHz and ω₀ = 1,000,000 rad/s
Engineering Notes
Tuned circuit applications
LC resonance is widely used in RF circuits, oscillators, filters, and impedance-matching networks.
Inductance shifts frequency
Increasing inductance lowers resonant frequency when capacitance remains constant.
Capacitance shifts frequency
Increasing capacitance lowers resonant frequency when inductance remains constant.
Parasitics and tolerance
Real inductors and capacitors include parasitic resistance, self-capacitance, ESR, and component tolerance.
Q factor and bandwidth
Q factor, loading, and losses determine practical bandwidth, selectivity, amplitude, and decay behavior.
Common Mistakes
- Entering µH or nF values as if they were base henries or farads.
- Ignoring component tolerance when a narrow tuning range is required.
- Using an inductor above its self-resonant frequency.
- Ignoring PCB trace inductance, pad capacitance, source impedance, and load damping.
Support reference
FAQ
What is LC resonance?
LC resonance is the natural oscillation that occurs as energy transfers between an inductor's magnetic field and a capacitor's electric field. An ideal LC circuit resonates at one frequency set by L and C.
How do you calculate resonant frequency in an LC circuit?
Use f₀ = 1 / (2π√(LC)), with inductance in henries and capacitance in farads. The result is the ideal resonant frequency in hertz.
What happens at resonant frequency?
At resonance, ideal inductive and capacitive reactances have equal magnitudes. Their interaction produces a frequency-selective impedance response that depends on whether the circuit is arranged in series or parallel.
How do inductance and capacitance affect resonance?
Increasing either inductance or capacitance lowers resonant frequency because f₀ is inversely proportional to the square root of their product. Reducing either value raises resonance.
What is the difference between series and parallel resonance?
An ideal series LC circuit has minimum impedance at resonance, while an ideal parallel LC circuit has maximum impedance. Practical behavior also depends on winding resistance, ESR, loading, and topology.
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Browse the Inductors calculator category or review related material in the Engineering Reference Center.
This calculator models an ideal lumped LC circuit. Confirm component tolerance, Q factor, self-resonance, parasitics, operating voltage and current, temperature, layout, and measured response before production use.