LC Resonance Calculator
Find the resonant frequency of an LC pair, plus XL, XC, and the net reactance at a test frequency.
🔒 Processed entirely in your browser — nothing you enter here is ever uploaded.
The result appears on this page after you run the tool. Nothing you enter is uploaded.
Result
About this tool
The form opens with inductance 10 and the unit menu on microhenries, capacitance 100 and the unit menu on nanofarads, and a test frequency of 1000 hertz. Those are the numbers the report uses until you change them. L is 10 × 10⁻⁶ = 0.00001 H and C is 100 × 10⁻⁹ = 1×10⁻⁷ F. Resonant frequency is 1 / (2π √(LC)). The product LC is 1×10⁻¹², its square root is 1×10⁻⁶, and 1 / (2π × 10⁻⁶) prints as 159.1549430919 kHz. All three of inductance, capacitance, and test frequency must be strictly positive or the report stops. The resistance box is not part of this frequency. A winding resistance you type later does not move the resonant number.
At the test frequency the page prints inductive reactance XL = 2πfL and capacitive reactance XC = 1 / (2πfC), then the net XL − XC. With the default 10 µH, 100 nF, and 1000 Hz, XL prints as 0.062831853071796 Ω and XC as 1.591549430919 kΩ. The net prints as −1.5914865990659 kΩ. The pair is capacitive at 1000 Hz because that test sits far below 159.15 kHz. At resonance XL and XC are equal and the net is zero, apart from floating-point residue. Changing the test frequency does not change the resonant-frequency line. It only changes XL, XC, and the net. The inductance unit menu also offers henries, millihenries, and nanohenries. Leaving the menu on microhenries and typing 10 is not the same as 10 millihenries.
If you also type a positive resistance, two more lines appear. Quality factor is √(L/C) / R, the series form, not the parallel form. Bandwidth is the resonant frequency divided by that Q. For the default 10 µH and 100 nF, √(L/C) is exactly 10. A series resistance of 10 Ω therefore prints Q as 1, and the bandwidth equals the resonant frequency, 159.1549430919 kHz. Leave the resistance box empty, or type a number that is not positive, and those two lines are omitted. A zero resistance would make the series Q infinite, so the page skips it instead of printing infinity. The model is a lumped series LC. The optional R is used only for Q and bandwidth. The page does not print an impedance magnitude that includes that R, does not plot a curve, and does not switch to a parallel tank. Parallel Q is a different formula and lives on the separate RLC page, which asks you to pick series or parallel. Component tolerance, the self-resonance of a real inductor, and the capacitor's ESR are not added to the frequency. The engineering formatter is why 159154.94 Hz appears as 159.1549430919 kHz rather than as a rounded hertz figure.
Example. The form opens at 10 µH and 100 nF, which resonate at 159.1549430919 kHz. At the default 1000 Hz test, XL is 0.062831853071796 Ω and XC is 1.591549430919 kΩ. Series R of 10 Ω adds Q 1 and bandwidth 159.1549430919 kHz.
Limit. Inductance, capacitance, and test frequency must be positive. The inductance unit menu opens on microhenries, not millihenries. Q and bandwidth appear only when series resistance is also positive, and that R does not shift the resonant frequency.
What do the default 10 µH and 100 nF give?
L is 0.00001 H and C is 1e-7 F. f = 1/(2π√(LC)) prints as 159.1549430919 kHz. The unit menu next to 10 is microhenries. Switching it to millihenries without changing the 10 would be a thousand times more inductance and a different frequency.
What do XL and XC mean at the test frequency?
XL is 2πfL and XC is 1/(2πfC), both at the frequency in the test box, which opens at 1000 Hz. With the default parts, XL is 0.062831853071796 Ω and XC is 1.591549430919 kΩ. Net reactance is XL minus XC, printed as −1.5914865990659 kΩ, so the pair is capacitive at that test frequency.
How is Q calculated when I enter a resistance?
Series Q is √(L/C) divided by R. For the default 10 µH and 100 nF, √(L/C) is 10, so 10 Ω of series resistance prints Q as 1 and bandwidth equal to the resonant frequency, 159.1549430919 kHz. If R is blank or not positive, those lines are left off. This is not the parallel formula.
Does this include the capacitor's ESR or a parallel tank?
No. Frequency is the ideal 1/(2π√(LC)). ESR is not added, and the page does not switch to a parallel circuit. The separate RLC page is the one with a series-or-parallel control.