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LC Tank Calculator

Electronics & PhysicsPhysics Reference
Solve for
Result —
Resonant frequency f
—
Inductance L
—
Capacitance C
—
Angular frequency ω
—
Period of one cycle
—
Reactance of L and C at resonance
—
Characteristic impedance √(L/C)
—

An LC tank resonates where the inductive and capacitive reactances are equal: f = 1 ÷ (2π√(LC)). For example, a 100 µH inductor with a 100 pF capacitor resonates at 1.592 MHz, and each component then has a reactance of 1 kΩ. Rearranged, the same relation gives the inductance or capacitance needed for a chosen frequency.

About this tool

Radio builders, filter designers and electronics students use an LC tank to set an oscillator frequency, tune a receiver front end or trap an unwanted signal. This calculator works in three directions: give it L and C and it returns the resonant frequency; give it a target frequency plus one component and it returns the other. Alongside the answer it lists the angular frequency, the period of one cycle, the reactance each part shows at resonance and the characteristic impedance √(L/C), which sets how a tank loads the circuit around it. Values are typed in with their own unit picker (nH to H, pF to F, Hz to GHz). The model is the ideal lossless tank: it ignores coil resistance, stray capacitance and component tolerance, so a real circuit lands a few percent away and usually needs a trimmer to finish tuning.

How to use it

  1. Pick what to solve for

    Choose resonant frequency, inductance or capacitance. Only the two inputs that mode needs are shown.

  2. Enter the known values

    Type each value and set its unit in the picker inside the field, for example µH and pF.

  3. Read the result and the working

    The headline gives the solved quantity in a sensible unit prefix; the stats list ω, period, reactance and √(L/C), and the steps show the substitution.

Examples

100 µH and 100 pF

Solve for
Resonant frequency
Inductance (L)
100
Inductance unit
µH
Capacitance (C)
100
Capacitance unit
pF

Result Result: 1.592 MHz
Resonant frequency f: 1.592 MHz
Inductance L: 100 µH
Capacitance C: 100 pF
Angular frequency ω: 10 Mrad/s
Period of one cycle: 628.3 ns
Reactance of L and C at resonance: 1 kΩ
Characteristic impedance √(L/C): 1 kΩ

  1. f = 1 ÷ (2π × √(100 µH × 100 pF)) = 1.592 MHz
  2. Reactance at resonance: X_L = X_C = 2πfL = 1 kΩ
  3. Characteristic impedance √(L ÷ C) = 1 kΩ

A common pairing for a tank near the top of the AM broadcast band. Each part has a reactance of 1 kΩ at resonance.

Inductor for 1 MHz with a 253.3 pF capacitor

Solve for
Inductance
Target frequency (f)
1
Frequency unit
MHz
Capacitance (C)
253.3
Capacitance unit
pF

Result Result: 100 µH
Resonant frequency f: 1 MHz
Inductance L: 100 µH
Capacitance C: 253.3 pF
Angular frequency ω: 6.283 Mrad/s
Period of one cycle: 1 µs
Reactance of L and C at resonance: 628.3 Ω
Characteristic impedance √(L/C): 628.3 Ω

  1. ω = 2π × 1 MHz = 6.283 Mrad/s
  2. L = 1 ÷ (ω² × C) = 1 ÷ (6.283 Mrad/s² × 253.3 pF) = 100 µH
  3. Reactance at resonance: X_L = X_C = 2πfL = 628.3 Ω
  4. Characteristic impedance √(L ÷ C) = 628.3 Ω

Rearranging the resonance formula as L = 1/(ω²C) gives 100 µH, the inductor that tunes 253.3 pF to 1 MHz.

How it is calculated

f = 1 ÷ (2π√(LC)); L = 1 ÷ (ω²C); C = 1 ÷ (ω²L); ω = 2πf

f
resonant frequency in hertz
L
inductance in henries
C
capacitance in farads
ω
angular frequency in radians per second

At resonance the inductor's reactance ωL equals the capacitor's reactance 1/(ωC). Setting them equal and solving gives ω = 1/√(LC), and dividing by 2π converts to hertz. The two rearranged forms follow from the same equality. The reactance at resonance equals √(L/C), the characteristic impedance, which is why the two stats match for every input. Every value is converted to base SI units before calculation and the results are shown to four significant figures.

When not to use it

  • Distributed circuits such as transmission-line stubs or cavities, where L and C are not lumped parts.
  • Finding bandwidth or Q, which needs the circuit's resistance as well.
  • Microwave designs above roughly 1 GHz, where pad and lead parasitics dominate.

Common mistakes

  • Mixing up µH and mH, which shifts the frequency by a factor of about 31.6.
  • Forgetting that stray and input capacitance add to the tuning capacitor.
  • Expecting frequency to scale linearly: doubling C lowers f only by a factor of √2.

Frequently asked questions

Why is the inductive reactance equal to √(L/C)?

At resonance ω = 1/√(LC). Multiply by L and the reactance ωL becomes L/√(LC), which simplifies to √(L/C). The capacitor's reactance 1/(ωC) reduces to the same quantity, which is the definition of resonance.

Does it matter whether L and C are in series or in parallel?

Not for the ideal resonant frequency. A series tank reaches minimum impedance and a parallel tank reaches maximum impedance at the same f = 1/(2π√(LC)). With real losses the parallel tank's peak shifts very slightly, usually by much less than component tolerance.

How much does a 5% capacitor tolerance move the frequency?

Frequency varies with the inverse square root of C, so a 5% change in capacitance moves f by roughly 2.5% in the opposite direction. The same holds for inductance, which is why precision tanks use a trimmer capacitor or an adjustable slug in the coil.

What capacitor tunes a 1 µH coil to 10.7 MHz?

About 221 pF. With ω = 2π × 10.7 MHz, C = 1/(ω²L) = 221.2 pF. In practice a fixed 180 pF part plus a trimmer covers the remaining value and the strays.

What does the characteristic impedance tell me?

√(L/C) sets the tank's impedance level. A tank with a high √(L/C) works with high-impedance circuits such as FET gates; a low value suits low-impedance loads. Combined with the circuit resistance it also determines the Q factor.

Why does my measured frequency come out lower than the result?

Stray capacitance from wiring, the PCB and the active device adds to C, and the coil has self-capacitance too. Those extra picofarads lower the frequency, especially when the tuning capacitor is small.

Cite this tool

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APA

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

MLA

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

Chicago

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

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