LC Circuit Frequency Calculator and Resonance Formula

An LC circuit frequency calculator finds the ideal resonant frequency from the circuit’s inductance and capacitance. Enter inductance in henries and capacitance in farads to get the frequency in hertz, along with its period and angular frequency.

Formula

The ideal resonant frequency of an LC circuit is f = 1 / (2π√(LC)). Here, f is frequency in hertz (Hz), L is inductance in henries (H), C is capacitance in farads (F), and π is approximately 3.14159. The formula assumes ideal components and no resistance or other parasitic effects.

The period is T = 1/f, measured in seconds per cycle, and angular frequency is ω = 2πf, measured in radians per second (rad/s). These are different ways of describing the same oscillation: frequency counts cycles each second, while angular frequency expresses phase change per second.

Worked Example

Using the calculator’s default values, L = 0.01 H (10 mH) and C = 0.000001 F (1 μF):

1. Multiply the component values: LC = 0.01 × 0.000001 = 0.00000001.
2. Take the square root: √LC = 0.0001.
3. Calculate the frequency: f = 1 / (2π × 0.0001) ≈ 1591.55 Hz, or 1.59 kHz.
4. Calculate the period: T = 1 / 1591.549… ≈ 0.000628 s.
5. Calculate angular frequency: ω = 2π × 1591.549… ≈ 10000.00 rad/s.

The calculator displays the headline frequency rounded to two decimal places: 1591.55 Hz.

How LC Resonance Works

An inductor stores energy in a magnetic field, while a capacitor stores energy in an electric field. In an ideal LC circuit, energy moves back and forth between those fields. The circuit’s natural oscillation rate is its resonant frequency, set by the product of inductance and capacitance.

A larger inductance or capacitance lowers the resonant frequency; a smaller value raises it. Since both values appear under the square root, changing either by a factor of four changes the frequency by a factor of two in the opposite direction. For example, doubling the capacitance lowers the frequency by 1/√2, not by half.

LC circuits appear in resonant and filtering applications, including oscillators and tuned circuits. The calculated value is a useful starting point for analysis, but a real circuit’s response also depends on its topology, losses, source, load, and component tolerances.

Entering Values and Reading Units

Use the units shown by the calculator, or convert the component values before entering them. Common prefixes are easy to confuse: 1 mH = 0.001 H, 1 μH = 0.000001 H, 1 μF = 0.000001 F, and 1 nF = 0.000000001 F. A value entered in microfarads as though it were farads can shift the result by a factor of 1000.

• Convert inductance to henries and capacitance to farads.
• Use positive component values. Zero or negative L or C does not describe an ordinary passive LC resonator under this formula.
• Read Hz as cycles per second; 1 kHz is 1000 Hz and 1 MHz is 1,000,000 Hz.
• Keep full precision for intermediate calculations, then round the displayed answer to a sensible number of digits.

The standard SI units are H and F. There is no separate US customary conversion needed for this calculation; component values are normally specified in these metric-derived electrical units.

Ideal Frequency Versus a Real Circuit

The formula gives the undamped natural frequency for an ideal LC combination. In practice, resistance dissipates energy, and components have tolerances and parasitic properties. These can affect the observed resonant peak, its width, and sometimes its location. At sufficiently high frequencies, wiring and component construction can also matter.

In a simple series RLC circuit, one often distinguishes the ideal LC natural frequency, 1/(2π√LC), from the damped oscillation frequency. For an underdamped series circuit, that oscillation frequency is √(1/(LC) − (R/(2L))²) in radians per second, where R is resistance in ohms. This expression applies only when the quantity under the square root is positive; other circuit arrangements have their own response equations. Do not treat the basic calculator result as a guarantee of a measured resonance.

Another common misconception is that an LC resonant circuit always oscillates by itself. The ideal equation describes a natural frequency, but a real circuit may need an initial energy input or an active circuit to sustain oscillations. Losses in passive components cause an unpowered oscillation to decay.

Frequently Asked Questions

What is the formula for the resonant frequency of an LC circuit?
Use f = 1/(2π√LC), with inductance in henries and capacitance in farads. The result is in hertz.

How do I calculate LC frequency in kHz?
Calculate the frequency in hertz, then divide by 1000. For example, 1591.55 Hz is about 1.59 kHz.

What happens to frequency if capacitance increases?
Frequency decreases according to the inverse square root of capacitance. If capacitance becomes four times larger while inductance stays constant, the ideal frequency becomes half as large.

Is angular frequency the same as frequency?
No. Frequency f is in cycles per second, while angular frequency ω is in radians per second. They are related by ω = 2πf.

Why might measured resonance differ from the calculator?
The calculator assumes ideal L and C. Resistance, component tolerances, parasitic capacitance or inductance, circuit loading, and measurement setup can shift or broaden the real response.

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in l | Inductance | H | 0.01 | 0
in c | Capacitance | F | 0.000001 | 0
out f | Resonant frequency | Hz | 1 / (2 * pi * sqrt(l * c)) | 2
out t | Period | s | 1 / f | 6
out w | Angular frequency | rad/s | 2 * pi * f | 2