LC Resonant Frequency

Enter L and C to compute resonance instantly. Includes unit conversions, reactance at resonance, and Show Work.

How to Use

  1. Enter Inductance (L) and Capacitance (C) with the correct units.
  2. Use “Solve For” if you want to solve for a missing variable (optional, via mode).
  3. Open “Show Work” to see the exact formulas and steps in base units.
  4. Use “Share Link” to generate a URL that restores these values (no auto URL updates while typing).
LC Lab View
Resonance summary: frequency, angular frequency, period, and reactance at f0.
f0
—
ω0
—
T
—
XL=XC
—
Status: —
C L Resonance occurs when XL = XC at f0 Outputs: f0 (Hz), ω0 (rad/s), period (s), and reactance magnitude at resonance (Ω).
Inputs & Settings
Enter L and C (or choose a solve mode). Results update instantly.
Examples: 100nH, 10µH, 250µH, 10mH
Examples: 10pF, 100pF, 10nF, 10µF
Used when solving for L or C from a desired f0
Loss model affects notes only unless JS adds Q/R features
Show Work (step-by-step)
—
Work is shown in base units (H, F, Hz, rad/s, s, Ω) for clarity and consistency.

LC Resonance Formulas

Resonant frequency: f0 = 1 / (2π√(L·C))

  • Angular frequency: ω0 = 2πf0 = 1 / √(L·C)
  • Period: T = 1 / f0
  • Reactance: XL = ωL, XC = 1/(ωC) and at resonance |XL| = |XC|
Where L = inductance (henry), C = capacitance (farad), f0 = hertz, ω0 = rad/s.

FAQ

What does resonance mean in an LC circuit?

Resonance is the frequency where the inductor and capacitor reactances cancel in magnitude (XL = XC), producing a peak (or notch) response depending on circuit topology.

Do real circuits resonate exactly at f0?

Real parts have resistance, parasitics, and tolerances. The “ideal” f0 is a baseline; measured resonance can shift.

Why can f0 be “invalid”?

If L ≤ 0 or C ≤ 0 (or missing required values for a solve mode), the resonance formula is not physically meaningful.

Tool Info

Last updated:

Updates may include improved unit handling, additional solve modes, and edge-case validation.