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LC Resonance Calculator

Electronics & PhysicsPhysics Reference

The coil or inductor value.

The capacitor value, including any stray capacitance you know of.

Resonant frequency f₀ —
Angular frequency ω₀
—
Period of one cycle
—
Reactance at resonance (X_L = X_C)
—
L × C product
—

An ideal LC circuit resonates at f₀ = 1 ÷ (2π√(LC)), where the inductive and capacitive reactances are equal and cancel. With L = 10 mH and C = 100 nF, LC = 10⁻⁹ s², √(LC) = 31.62 µs and the resonant frequency is 5.033 kHz, with each reactance equal to 316.2 Ω.

About this tool

Radio hobbyists winding a tuning coil, students checking a lab tank circuit and engineers sizing a passive filter all need the same number: the frequency at which an inductor and a capacitor trade energy back and forth. Enter the inductance and capacitance, each with its own unit from henries down to nanohenries and farads down to picofarads, and the resonant frequency appears with an automatic metric prefix. Alongside it you get the angular frequency in rad/s, the period of one oscillation, the reactance of either part at resonance (also called the characteristic impedance) and the L × C product. The working shows each step of the Thomson formula. The model is ideal: it ignores coil resistance, so it gives no Q factor or bandwidth, and at very high frequencies stray capacitance and lead inductance shift the real resonance.

How to use it

  1. Enter the inductance

    Type the coil value and pick H, mH, µH or nH from the unit list inside the field.

  2. Enter the capacitance

    Type the capacitor value and choose F, µF, nF or pF beside it.

  3. Read the frequency and extras

    The resonant frequency, angular frequency, period and reactance update as you type; open the working to follow the arithmetic.

Examples

1 H and 1 µF

Inductance (L)
1
Inductance unit
H
Capacitance (C)
1
Capacitance unit
µF

Result Resonant frequency f₀: 159.2 Hz
Angular frequency ω₀: 1 krad/s
Period of one cycle: 6.283 ms
Reactance at resonance (X_L = X_C): 1 kΩ
L × C product: 1.0000e-6 s²

  1. L = 1 H, C = 1 µF, L × C = 1.0000e-6 s²
  2. √(L × C) = 1.0000e-3 s
  3. f₀ = 1 ÷ (2π × 1.0000e-3) = 159.2 Hz
  4. ω₀ = 2π × f₀ = 1 krad/s
  5. X_L = X_C = √(L ÷ C) = 1 kΩ

A textbook pairing: √(LC) is exactly 1 ms, so the circuit rings at 1000 ÷ 2π, just under 160 Hz, and each reactance is 1 kΩ there.

10 mH and 100 nF audio-band tank

Inductance (L)
10
Inductance unit
mH
Capacitance (C)
100
Capacitance unit
nF

Result Resonant frequency f₀: 5.033 kHz
Angular frequency ω₀: 31.62 krad/s
Period of one cycle: 198.7 µs
Reactance at resonance (X_L = X_C): 316.2 Ω
L × C product: 1.0000e-9 s²

  1. L = 10 mH, C = 100 nF, L × C = 1.0000e-9 s²
  2. √(L × C) = 3.1623e-5 s
  3. f₀ = 1 ÷ (2π × 3.1623e-5) = 5.033 kHz
  4. ω₀ = 2π × f₀ = 31.62 krad/s
  5. X_L = X_C = √(L ÷ C) = 316.2 Ω

L × C is 10⁻⁹ s², giving a resonance near 5 kHz, typical of a passive audio filter or notch.

100 µH and 100 pF in the AM band

Inductance (L)
100
Inductance unit
µH
Capacitance (C)
100
Capacitance unit
pF

Result Resonant frequency f₀: 1.592 MHz
Angular frequency ω₀: 10 Mrad/s
Period of one cycle: 628.3 ns
Reactance at resonance (X_L = X_C): 1 kΩ
L × C product: 1.0000e-14 s²

  1. L = 100 µH, C = 100 pF, L × C = 1.0000e-14 s²
  2. √(L × C) = 1.0000e-7 s
  3. f₀ = 1 ÷ (2π × 1.0000e-7) = 1.592 MHz
  4. ω₀ = 2π × f₀ = 10 Mrad/s
  5. X_L = X_C = √(L ÷ C) = 1 kΩ

√(LC) is 0.1 µs, so the tank tunes to about 1.59 MHz, near the top of the medium-wave broadcast band.

How it is calculated

f₀ = 1 ÷ (2π × √(L × C)); ω₀ = 2π × f₀; X = √(L ÷ C)

L
inductance in henries
C
capacitance in farads
f₀
resonant frequency in hertz
ω₀
angular resonant frequency in radians per second
X
reactance of L or C at resonance, in ohms

Resonance happens where the inductive reactance 2πfL equals the capacitive reactance 1 ÷ (2πfC). Setting them equal and solving for f gives the Thomson formula. Both values are first converted to base SI units, multiplied, square-rooted and inverted. Substituting f₀ back into either reactance gives √(L ÷ C), the characteristic impedance of the tank. The same frequency applies to series and parallel LC circuits when resistance is negligible.

When not to use it

  • Do not rely on it for a lossy coil where the series resistance is large compared with √(L/C).
  • It cannot give Q factor, bandwidth or damping, since no resistance is entered.
  • Above a few hundred megahertz, PCB traces and leads change L and C enough that a field solver or measurement is needed.

Common mistakes

  • Mixing up µH and mH, which shifts the frequency by a factor of about 31.6.
  • Forgetting that the result is in hertz, not rad/s; ω₀ is 2π times larger.
  • Ignoring stray and probe capacitance when the tuning capacitor is only a few picofarads.
  • Expecting the frequency to scale linearly: doubling C lowers f₀ only by a factor of √2.

Frequently asked questions

Why does the frequency depend on the square root of LC?

At resonance 2πfL = 1/(2πfC), which rearranges to f² = 1/(4π²LC). Taking the square root gives f = 1/(2π√LC). So to halve the frequency you must make the LC product four times larger, for example by quadrupling the capacitance.

Is the resonant frequency the same for series and parallel LC circuits?

For ideal components, yes. Both resonate where the two reactances are equal. The difference is in behaviour: a series circuit shows minimum impedance at resonance, while a parallel tank shows maximum impedance. With real coil resistance the parallel resonance shifts slightly, which this calculator does not model.

What is the reactance at resonance telling me?

It is √(L/C), the impedance of either component at f₀, also called the characteristic impedance. It sets how much circulating current flows for a given voltage and, combined with circuit resistance, determines the Q factor. A 1 H and 1 µF pair has 1 kΩ reactance at 159.2 Hz.

How do I find the capacitor needed for a target frequency?

Rearrange the formula: C = 1/(4π²f²L). For 1 MHz with a 100 µH coil, C = 1/(39.48 × 10¹² × 10⁻⁴) ≈ 253 pF. You can also try values in the capacitance field until the frequency matches the target.

Why does my measured resonance come out lower than calculated?

Real circuits add capacitance you did not enter: the coil's own winding capacitance, PCB pads, probe tips and transistor junctions. All of it adds to C and pulls the frequency down. Inductor tolerances of 5 to 20 percent also move the result.

What does the period output mean?

It is the time for one full oscillation, 1/f₀. For a 5.033 kHz tank the period is about 198.7 µs. It is handy when checking a ringing waveform on an oscilloscope, where you measure time between peaks rather than frequency.

Cite this tool

Using this tool in an assignment, article or report? Copy a citation, or a link for your website.

APA

Tools Directory Editorial Team. (2026, October 23). LC Resonance Calculator. Tools Directory. Retrieved October 27, 2026, from https://tools.milunir.com/electronics-physics/physics-reference/lc-resonance-calculator/

MLA

Tools Directory Editorial Team. “LC Resonance Calculator.” Tools Directory, 23 Oct. 2026, https://tools.milunir.com/electronics-physics/physics-reference/lc-resonance-calculator/. Accessed 27 Oct. 2026.

Chicago

Tools Directory Editorial Team. “LC Resonance Calculator.” Tools Directory. Last modified October 23, 2026. Accessed October 27, 2026. https://tools.milunir.com/electronics-physics/physics-reference/lc-resonance-calculator/.

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