LC Resonant Frequency Calculator
Enter the inductance and capacitance of your LC circuit to find the resonant frequency, angular frequency and period.
Reviewed by the ToolNestr Editorial Team — July 2026
How LC resonant frequency is calculated
The resonant frequency of an LC circuit is determined by the Thomson formula: f = 1 / (2π√(LC)), where L is inductance in henries and C is capacitance in farads. The frequency is inversely proportional to the square root of both L and C — doubling either value reduces the frequency by a factor of √2.
The angular frequency ω = 1 / √(LC) (measured in radians per second) and the period T = 1 / f are also displayed. At resonance, inductive reactance XL = 2πfL equals capacitive reactance XC = 1/(2πfC).
Worked example
Frequency bands for LC circuits
LC circuits are used across a wide range of frequencies. Different component values are needed for different frequency bands.
RF Engineer
Design antenna matching networks, filters and oscillators for wireless communication systems with precise frequency targets.
Audio Crossover Designer
Calculate LC values for speaker crossover networks to split audio signals between tweeters, midranges and woofers.
Ham Radio Operator
Build and tune resonant circuits for your amateur radio equipment, from crystal filters to tank circuits in transmitters.
Electronics Student
Explore the relationship between inductance, capacitance and resonant frequency in foundational circuit analysis.
| Inductance | Capacitance | Resonant frequency | Application |
|---|---|---|---|
| 10 \u00b5H | 100 pF | 5.03 MHz | Shortwave radio |
| 100 \u00b5H | 100 pF | 1.59 MHz | AM radio |
| 1 mH | 1 nF | 159 kHz | Longwave |
| 1 mH | 10 \u00b5F | 1.59 kHz | Audio crossover |
| 10 \u00b5H | 10 pF | 15.9 MHz | FM radio / VHF |
| 1 \u00b5H | 10 pF | 50.3 MHz | VHF TV |
How to use the LC Resonant Frequency Calculator
Enter inductance
Type the inductor value and select the correct unit (\u00b5H, mH or H). Most RF inductors are in the microhenry (\u00b5H) range.
Enter capacitance
Type the capacitor value with the correct unit (pF, nF or \u00b5F). Small capacitors in the pF range are typical for RF applications.
Read the results
The calculator instantly shows the resonant frequency, angular frequency and period \u2014 all three values update as you type.
Tips for working with LC circuits
Account for parasitic capacitance
Every inductor has self-capacitance between its windings, which creates self-resonance. Above this frequency, the inductor behaves like a capacitor. Choose inductors with self-resonant frequency well above your operating frequency.
Use a trimmer capacitor for tuning
For adjustable resonant circuits, use a trimmer capacitor (typically 5-50 pF) in parallel with a fixed capacitor. This allows fine-tuning the resonant frequency to compensate for component tolerances and PCB parasitics.
Minimize stray inductance and capacitance
Keep leads short and use ground planes to minimize stray inductance and capacitance that shift the resonant frequency. Surface-mount components have significantly lower parasitics than through-hole parts at RF frequencies.
Consider the impedance at resonance
The impedance of a parallel LC tank circuit at resonance is Z = L/(RC), where R is the series resistance of the inductor. Higher Q means higher impedance. For matching networks, this impedance determines how well the circuit couples to the load.
The LC resonance formula: f = 1 / (2\u03c0\u221a(LC))
The resonant frequency of an LC circuit is determined by the Thomson formula f = 1/(2\u03c0\u221a(LC)). This equation shows that frequency is inversely proportional to the square root of both L and C. Doubling inductance reduces frequency by a factor of \u221a2. The formula works for both series and parallel resonant circuits; what changes is the impedance behavior, not the resonant frequency itself.
Applications of LC resonant circuits
LC resonant circuits are everywhere in electronics. In radio receivers, they select the desired station while rejecting others. In oscillators, they set the operating frequency for transmitters and clock generators. In filter design, they pass or block specific frequency bands. In power electronics, they enable resonant converters with high efficiency and low switching losses. In audio, they split signals between speaker drivers in crossover networks.
Understanding inductor and capacitor behavior
At resonance, the inductive reactance (X\u2097 = 2\u03c0fL) equals the capacitive reactance (X\u1d04 = 1/(2\u03c0fC)). Below resonance, X\u1d04 dominates and the circuit behaves capacitively. Above resonance, X\u2097 dominates and the circuit behaves inductively. In a series LC circuit, impedance is minimum at resonance. In a parallel LC circuit, impedance is maximum at resonance.
Quality factor and bandwidth
The Q factor determines the bandwidth of the resonant circuit: BW = f\u2080/Q. A high Q circuit has a narrow bandwidth and sharp selectivity, ideal for radio tuners. A lower Q circuit has wider bandwidth, useful for audio applications. Q is primarily limited by the inductor\u2019s series resistance. Air-core inductors have higher Q than ferrite-core types but are physically larger.
Frequently asked questions
What is the resonant frequency of an LC circuit?
The resonant frequency is the frequency at which an LC circuit naturally oscillates with maximum amplitude. It is given by the formula f = 1 / (2π√(LC)), where L is inductance in henries and C is capacitance in farads.
How do I calculate the resonant frequency?
To calculate resonant frequency, multiply L and C, take the square root, multiply by 2π, then take the reciprocal. For example, with L = 10 µH and C = 100 pF: f = 1 / (2π × √(10×10⁻⁶ × 100×10⁻¹²)) ≈ 5.03 MHz.
What is angular frequency in an LC circuit?
Angular frequency ω = 2πf, measured in radians per second. It is the rate of change of the sinusoidal waveform in the tank circuit. The formula is ω = 1 / √(LC). It is commonly used in filter design and signal analysis.
What are tank circuits used for?
LC tank circuits are fundamental in radio frequency design. They are used in radio tuners (selecting stations), oscillators (generating carrier waves), bandpass filters (passing specific frequencies), and impedance matching networks.
How do I choose L and C values for a specific frequency?
Use the formula LC = 1/(2πf)². For a given frequency, there are infinite L/C combinations. Larger L with smaller C gives higher impedance; smaller L with larger C gives lower impedance. The choice depends on your circuit impedance requirements.
What is the Q factor of an LC circuit?
The Q factor (Quality factor) measures the sharpness of resonance. Q = ωL/R for a series resonant circuit. Higher Q means narrower bandwidth and better frequency selectivity. Practical LC circuits have Q factors from 10 to several hundred.
Does the resonant frequency change with load?
Yes. Connecting a load to the LC circuit alters its effective impedance and can shift the resonant frequency slightly. External capacitance from traces and components also adds to the total capacitance, lowering the frequency.
What is the difference between series and parallel resonance?
In series resonance, impedance is minimum at the resonant frequency. In parallel resonance, impedance is maximum. Series LC circuits are used for bandpass filtering, while parallel LC circuits (tank circuits) are used in oscillators and RF amplifiers.
How does temperature affect LC resonance?
Inductors and capacitors have temperature coefficients. As temperature changes, component values drift, shifting the resonant frequency. NP0/C0G capacitors and air-core inductors offer the best temperature stability for precision circuits.
Can I use this calculator for audio crossover design?
Yes. LC resonant circuits are used in audio crossover networks to split frequencies between speakers. For example, a 1 mH inductor with a 10 µF capacitor resonates at about 1.59 kHz, suitable for a midrange crossover point.
Sources & references
This tool uses standard formulas and reference values from:
- • NFPA 70 — National Electrical Code (NEC), conduit fill, box fill and conductor ampacity. nfpa.org
- • IPC-2221, Generic Standard on Printed Board Design (trace width / current). ipc.org
- • NIST reference constants and unit definitions; IEEE standards where applicable. nist.gov
For educational and preliminary use. Verify against full engineering calculations and the governing standard before any real design.