LC Resonance CalculatorFree online other calculator — instant results, no sign-up
Calculate ideal resonant frequency from inductance and capacitance.
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About the LC Resonance Calculator
The LC Resonance Calculator finds the ideal resonant frequency of an inductor–capacitor circuit from inductance in millihenries and capacitance in nanofarads. Use it to estimate the natural oscillation frequency of an ideal LC circuit before accounting for component losses and parasitic effects.
- Inductance (mH)
- The inductor’s inductance in millihenries (mH), with a default of 10 mH.
- Capacitance (nF)
- The capacitor’s capacitance in nanofarads (nF), with a default of 100 nF.
Formula and method
f₀ = 1 / (2π√(LC)), where L = L_mH × 10⁻³ and C = C_nF × 10⁻⁹; for the defaults, f₀ = 1 / (2π√((10 × 10⁻³)(100 × 10⁻⁹))) = 5,032.92121 Hz.
- f₀Ideal resonant frequency in hertz (Hz).
- LInductance converted to henries (H).
- CCapacitance converted to farads (F).
- L_mHThe entered inductance value in millihenries.
- C_nFThe entered capacitance value in nanofarads.
- πThe mathematical constant pi, approximately 3.14159.
Convert both inputs to SI units, multiply L by C, take the square root, and divide 1 by 2π times that square root. With 10 mH and 100 nF, L = 0.01 H and C = 0.0000001 F, so LC = 10⁻⁹ H·F. Applying the formula gives 5,032.92121 Hz after rounding.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Inductance10 mH
- Capacitance100 nF
Results
- Result5,032.92121 Hz
How to use the LC Resonance Calculator
- 1Enter a positive inductance in the Inductance (mH) field; keep 10 for the default example.
- 2Enter a positive capacitance in the Capacitance (nF) field; keep 100 for the default example.
- 3Confirm that your component values are expressed in mH and nF, converting them first if necessary.
- 4Run the calculation to obtain the ideal resonant frequency.
- 5Read the Result row in hertz; the default inputs produce 5,032.92121 Hz.
Reading your result
The Result row reports the ideal resonant frequency in Hz, or cycles per second. For 10 mH and 100 nF, the result is 5,032.92121 Hz, approximately 5.033 kHz. At this frequency, the ideal inductor and capacitor have equal reactance magnitudes; an ideal series LC branch has zero net reactance, while an ideal parallel LC branch has zero net susceptance.
Limitations
The calculation assumes positive, finite inductance and capacitance and ideal lumped components. It ignores resistance, capacitor losses, inductor self-capacitance, wiring parasitics, loading, and component tolerances. These effects can shift measured resonance and alter its sharpness. The calculator does not determine bandwidth, quality factor, impedance, or voltage and current levels, and the displayed decimal places do not imply equivalent physical accuracy.
Common questions
Why must mH and nF be converted before using the resonance formula?+
The formula gives frequency in Hz when inductance is in H and capacitance is in F. The default 10 mH becomes 0.01 H, and 100 nF becomes 0.0000001 F.
How does increasing inductance or capacitance affect LC resonance?+
The resonant frequency decreases as either value increases because f₀ is proportional to 1/√(LC). Doubling either component value while holding the other fixed reduces the frequency by a factor of √2.
Does this formula apply to both series and parallel LC circuits?+
Yes, ideal series and parallel LC circuits share the frequency 1/(2π√(LC)). Their impedance behavior differs: an ideal series LC branch has minimum impedance at resonance, while an ideal parallel LC branch has maximum impedance.
Why might my measured resonance differ from 5,032.92121 Hz?+
That result assumes exactly 10 mH and 100 nF with no losses or parasitics. Real component tolerances, frequency-dependent inductance, stray capacitance, resistance, and measurement loading can make the observed resonance differ.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.