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LC Resonance Calculator

Computes the resonant frequency of an inductor–capacitor circuit from L and C, or solves for the inductance or capacitance needed to resonate at a given frequency, plus the angular frequency and characteristic impedance √(L/C).

When to use

You are designing or analysing a tuned circuit, oscillator tank, RF filter or antenna trap and know two of inductance, capacitance and frequency.

Do not use when: Resistance matters (bandwidth and Q need the series/parallel resistance), or you have only R and C (use rc-time-constant).

Formula

resonant_frequency_hz = 1 / (2π √(L × C)) with L = inductance_uh × 1e-6 H and C = capacitance_pf × 1e-12 F; L = 1 / ((2π f)² C); C = 1 / ((2π f)² L); characteristic_impedance_ohm = √(L / C)

Inputs

Parameter	Type	Unit	Required	Description
`inductance_uh`	number	µH	no	Inductance in microhenries (1 mH = 1000 µH, 1 nH = 0.001 µH). Omit to solve for it. Range: > 0
`capacitance_pf`	number	pF	no	Capacitance in picofarads (1 nF = 1000 pF, 1 µF = 1e6 pF). Omit to solve for it. Range: > 0
`frequency_hz`	number	Hz	no	Resonant frequency in hertz (1 kHz = 1000, 1 MHz = 1e6). Omit to solve for it. Range: > 0

Outputs

Output	Type	Unit	Description
`solved_for`	string		Which quantity was computed: frequency_hz, inductance_uh or capacitance_pf.
`resonant_frequency_hz`	number	Hz	f₀ = 1 / (2π √(L C)).
`resonant_frequency_khz`	number	kHz	f₀ in kilohertz.
`resonant_frequency_mhz`	number	MHz	f₀ in megahertz.
`angular_frequency_rad_s`	number	rad/s	ω₀ = 2π f₀ = 1 / √(L C).
`inductance_uh`	number	µH	L = 1 / ((2π f)² C).
`capacitance_pf`	number	pF	C = 1 / ((2π f)² L).
`characteristic_impedance_ohm`	number	Ω	√(L / C), the reactance of L and of C at resonance.

Example

100 µH with 100 pF: {"inductance_uh":100,"capacitance_pf":100} → {"solved_for":"frequency_hz","resonant_frequency_hz":1591549.43,"resonant_frequency_mhz":1.591549,"angular_frequency_rad_s":10000000,"characteristic_impedance_ohm":1000}

Capacitor for 1 MHz with 10 µH: {"inductance_uh":10,"frequency_hz":1000000} → {"solved_for":"capacitance_pf","capacitance_pf":2533.0296,"characteristic_impedance_ohm":62.8319,"resonant_frequency_khz":1000}

GET https://tttkmbb.com/api/v1/calculate/lc-resonance?inductance_uh=100&capacitance_pf=100

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/lc-resonance (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/lc-resonance · Markdown: https://tttkmbb.com/engineering/lc-resonance.md · JSON definition: https://tttkmbb.com/engineering/lc-resonance.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="lc-resonance"
OpenAPI operationId: solve_lc_resonance
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – LC circuit (reference)
HyperPhysics – Series resonance (reference)

FAQ

Does resistance change the resonant frequency?

Only slightly for a series RLC (f₀ is unchanged); in a parallel tank with coil resistance the peak shifts down a little. Resistance mainly sets the bandwidth f₀/Q.

Why does the same L·C product give the same frequency?

Only the product L·C fixes f₀; the ratio L/C sets the characteristic impedance, which determines the voltages and currents at resonance.

Related calculators

RC Time Constant Calculator — Time constant and cutoff of an RC pair.
Wavelength & Frequency Calculator — Wavelength of the resonant frequency.
Frequency Converter — Convert between Hz, kHz, MHz and GHz.