An LC circuit is one of the fundamental building blocks of electronics and electrical engineering. It uses two energy-storage components—an inductor (L) and a capacitor (C)—to create electrical oscillations and frequency-selective behavior. Understanding the relationship between inductance and capacitance is important when designing resonant circuits, filters, oscillators, tuning networks, and many other electronic systems.

The LC Circuit Calculator makes these calculations much easier. Instead of manually converting units and working through several equations, you can enter an inductance and capacitance value, select their respective units, and quickly determine the circuit's resonant frequency, angular frequency, inductive reactance, and capacitive reactance.

The calculator supports inductance in henries (H), millihenries (mH), and microhenries (µH). Capacitance can be entered in farads (F), millifarads (mF), microfarads (µF), or nanofarads (nF). This makes the tool useful for a wide range of circuit calculations, from introductory electronics exercises to practical component selection and circuit analysis.

This guide explains what an LC circuit is, how the calculator works, the formulas behind the results, how to use the tool, worked examples, unit conversions, and important considerations when interpreting LC circuit calculations.

What Is an LC Circuit?

An LC circuit is an electrical circuit containing an inductor and a capacitor. The name "LC" comes directly from the conventional symbols used for these two components:

• L represents inductance.
• C represents capacitance.

The inductor stores energy in a magnetic field, while the capacitor stores energy in an electric field. When connected together, energy can move back and forth between these two components, creating an oscillating electrical response.

In an ideal LC circuit, this energy exchange can continue indefinitely. Real-world circuits, however, contain resistance and other losses, so practical oscillations gradually decrease unless energy is supplied to the circuit.

The frequency at which an LC circuit naturally oscillates is called its resonant frequency.

This frequency depends primarily on the values of the inductance and capacitance.

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What Is Resonance in an LC Circuit?

Resonance occurs when the inductive and capacitive effects of the circuit balance each other at a particular frequency.

The resonant angular frequency is:$$\omega_0 = \frac{1}{\sqrt{LC}}$$

where:

• $\omega_0$ = resonant angular frequency in radians per second
• $L$ = inductance in henries
• $C$ = capacitance in farads

The ordinary resonant frequency is:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

where:

• $f_0$ = resonant frequency in hertz
• $L$ = inductance in henries
• $C$ = capacitance in farads
• $\pi$ ≈ 3.14159

These are the central equations used by the LC Circuit Calculator.

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How to Use the LC Circuit Calculator

The calculator is designed to make the calculation process straightforward.

Step 1: Enter the Inductance

Enter the value of the inductor in the Inductance (L) field.

You can select:

• H
• mH
• µH

For example, if your inductor is rated at 10 millihenries, enter:

10

and select:

mH

The calculator converts the value to henries before performing the calculations.

Step 2: Enter the Capacitance

Enter the capacitor value in the Capacitance (C) field.

The available units are:

• F
• mF
• µF
• nF

For example, for a 100 µF capacitor, enter:

100

and select:

µF

The calculator converts the value to farads automatically.

Step 3: Click Calculate

After entering both component values, click Calculate.

The calculator checks that both values are greater than zero and then calculates the requested circuit characteristics.

Step 4: Review the Results

The calculator displays four results:

1. Resonant Frequency
2. Angular Frequency
3. Inductive Reactance
4. Capacitive Reactance

These values provide a useful snapshot of the LC circuit's behavior at resonance.

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LC Circuit Formulas Explained

Understanding the formulas can help you interpret the calculator's results rather than simply accepting the numbers.

1. Resonant Angular Frequency

The first major calculation is angular frequency:$$\omega_0 = \frac{1}{\sqrt{LC}}$$

The units are radians per second (rad/s).

Angular frequency describes oscillation in terms of angular motion rather than cycles per second.

For example, an angular frequency of 10,000 rad/s corresponds to an ordinary frequency of approximately:$$f = \frac{10,000}{2\pi}$$

which is about 1,591.55 Hz.

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2. Resonant Frequency

The ordinary resonant frequency is calculated using:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

The result is expressed in hertz (Hz).

One hertz means one cycle per second.

For example:

• 1 Hz = 1 cycle per second
• 1 kHz = 1,000 cycles per second
• 1 MHz = 1,000,000 cycles per second

The calculator displays the resonant frequency using scientific notation when appropriate, which is particularly useful when working with very small inductances or capacitances.

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How Inductance Affects Resonant Frequency

Inductance and capacitance have an inverse relationship with resonant frequency.

From:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

if inductance increases while capacitance remains constant, the resonant frequency decreases.

Conversely, reducing inductance increases the resonant frequency.

For example, suppose capacitance remains unchanged and inductance changes from 10 µH to 100 µH. Because the inductance is larger, the resulting resonant frequency will be lower.

This relationship is useful when selecting components for a target frequency.

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How Capacitance Affects Resonant Frequency

Capacitance behaves similarly.

Increasing capacitance lowers the resonant frequency, while decreasing capacitance raises it.

This is why variable capacitors can be useful in tuning circuits. Adjusting capacitance changes the resonant frequency of the LC network.

The relationship is:$$f_0 \propto \frac{1}{\sqrt{C}}$$

Therefore, the resonant frequency does not change linearly with capacitance. A fourfold increase in capacitance, for example, results in the resonant frequency becoming half as large when inductance remains constant.

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Inductive Reactance Formula

The calculator also determines inductive reactance.

Inductive reactance is calculated as:$$X_L = 2\pi fL$$

where:

• $X_L$ = inductive reactance in ohms
• $f$ = frequency in hertz
• $L$ = inductance in henries

Inductive reactance represents the opposition an inductor provides to alternating current.

Unlike ordinary resistance, inductive reactance depends on frequency.

As frequency increases, inductive reactance increases.

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Capacitive Reactance Formula

Capacitive reactance is calculated using:$$X_C = \frac{1}{2\pi fC}$$

where:

• $X_C$ = capacitive reactance in ohms
• $f$ = frequency in hertz
• $C$ = capacitance in farads

Capacitive reactance behaves in the opposite direction to inductive reactance.

As frequency increases, capacitive reactance decreases.

This opposite behavior between inductors and capacitors is central to LC resonance.

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Why Inductive and Capacitive Reactance Are Equal at Resonance

At the ideal resonant frequency:$$X_L = X_C$$

This relationship follows directly from the resonance condition.

For the inductor:$$X_L = 2\pi fL$$

For the capacitor:$$X_C = \frac{1}{2\pi fC}$$

At resonance, setting these equal gives:$$2\pi fL = \frac{1}{2\pi fC}$$

Rearranging:$$(2\pi f)^2LC = 1$$

and therefore:$$f = \frac{1}{2\pi\sqrt{LC}}$$

This is the resonant-frequency formula used by the calculator.

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Worked Example: Finding LC Resonance

Suppose you have:

• Inductance = 10 µH
• Capacitance = 100 nF

We first convert the values into SI units.

Convert inductance

Since:$$1\ \mu H = 0.000001\ H$$

then:$$10\ \mu H = 10 \times 0.000001$$$$L = 0.00001\ H$$

Convert capacitance

Since:$$1\ nF = 0.000000001\ F$$

then:$$100\ nF = 100 \times 0.000000001$$$$C = 0.0000001\ F$$

Now use the resonant-frequency formula:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

Substituting the values gives a resonant frequency of approximately:

159.15 kHz

The corresponding angular frequency is approximately:

1.00 × 10⁶ rad/s

At resonance, the inductive and capacitive reactances are approximately equal. For these component values, each reactance is approximately:

10 Ω

This demonstrates how the calculator converts component values and produces the important circuit characteristics automatically.

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Example Calculation Table

Here are some illustrative LC combinations and their approximate resonant frequencies.

Inductance	Capacitance	Approx. Resonant Frequency
1 µH	100 pF	15.92 MHz
10 µH	100 pF	5.03 MHz
10 µH	1 nF	1.59 MHz
10 µH	100 nF	159.15 kHz
100 µH	100 nF	50.33 kHz
1 mH	1 µF	5.03 kHz
10 mH	10 µF	503.29 Hz

These values illustrate an important principle: larger inductance or larger capacitance generally produces a lower resonant frequency.

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LC Unit Conversion Reference

The calculator supports common inductance and capacitance units.

Inductance Units

Unit	Equivalent in Henries
1 H	1 H
1 mH	0.001 H
1 µH	0.000001 H

For example:

25 mH = 0.025 H

and:

50 µH = 0.00005 H

Capacitance Units

Unit	Equivalent in Farads
1 F	1 F
1 mF	0.001 F
1 µF	0.000001 F
1 nF	0.000000001 F

For example:

10 µF = 0.00001 F

and:

100 nF = 0.0000001 F

Correct unit conversion is essential because the resonance formula requires inductance in henries and capacitance in farads.

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What Does Angular Frequency Mean?

Angular frequency can initially seem confusing because it is not measured in ordinary cycles per second.

It is represented by the Greek letter ω and is measured in radians per second.

The relationship between angular frequency and ordinary frequency is:$$\omega = 2\pi f$$

Therefore:$$f = \frac{\omega}{2\pi}$$

For example, if:$$\omega = 1,000\ rad/s$$

then:$$f = \frac{1,000}{2\pi}$$

which is approximately:

159.15 Hz

The calculator reports both measurements so that you can use whichever form is appropriate for your circuit analysis.

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Understanding Reactance in an LC Circuit

Reactance is different from resistance, even though both are measured in ohms.

Resistance represents opposition to current that dissipates electrical energy, generally as heat.

Reactance represents opposition associated with energy storage in inductors and capacitors.

Inductor

For an inductor:$$X_L = 2\pi fL$$

As frequency increases, $X_L$ increases.

Capacitor

For a capacitor:$$X_C = \frac{1}{2\pi fC}$$

As frequency increases, $X_C$ decreases.

At resonance, the magnitudes become equal in an ideal LC circuit.

This balance is one of the most important characteristics of resonant circuits.

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Common Applications of LC Circuits

LC circuits appear throughout electrical and electronic systems.

Radio Tuning

LC networks can be used to select particular frequencies from a range of radio signals. Changing the inductance or capacitance changes the resonant frequency.

Filters

LC combinations are used in frequency-selective circuits that allow some frequencies to pass while reducing others.

Oscillators

LC resonators can provide frequency-determining behavior in oscillator circuits.

Impedance Matching

LC networks can help transform impedances between circuit sections, particularly in radio-frequency applications.

Signal Processing

Resonant LC networks can be used to emphasize or reject selected frequency ranges.

Wireless and RF Electronics

Inductors and capacitors are fundamental components in many radio-frequency circuits, antenna networks, matching networks, and resonant structures.

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Series and Parallel LC Circuits

The same basic resonance relationship applies to ideal LC combinations, but the way the circuit behaves depends on how the components are connected.

Series LC Circuit

In a series LC circuit, the inductor and capacitor are connected in series.

At resonance, their reactances have equal magnitude and opposite phase contributions. The reactive effects cancel in the ideal case.

Parallel LC Circuit

In a parallel LC circuit, the inductor and capacitor are connected in parallel.

The resonance behavior is different from a series circuit in terms of current and impedance characteristics, but the ideal resonant frequency is still determined by the same fundamental LC relationship:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

The calculator focuses on the ideal LC resonance calculation rather than detailed circuit topology, losses, or impedance characteristics.

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Ideal LC Circuit vs. Real-World Circuit

The calculator uses the standard ideal LC equations.

Real circuits are more complicated.

Actual inductors have:

• Winding resistance
• Parasitic capacitance
• Core losses in some designs
• Frequency-dependent characteristics

Actual capacitors can have:

• Equivalent series resistance (ESR)
• Leakage
• Parasitic inductance
• Dielectric losses

Because of these factors, the measured resonance of a physical circuit can differ from a simple theoretical calculation.

The calculator should therefore be viewed as a theoretical LC resonance calculator based on the supplied inductance and capacitance values.

For high-frequency, precision, or engineering-critical designs, component tolerances and parasitic effects should also be considered.

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Component Tolerance and Resonant Frequency

Real inductors and capacitors are manufactured with tolerances.

Suppose a capacitor is labeled 100 nF but has a tolerance of ±10%. Its actual capacitance may differ from the nominal value.

Because:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

a change in either L or C changes the resonant frequency.

This means that two circuits built with nominally identical components may not resonate at exactly the same frequency.

For applications requiring precise frequency control, designers may use tighter-tolerance components, adjustable components, calibration, or measurement.

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How to Choose L and C for a Desired Frequency

The LC resonance formula can also be rearranged when designing a circuit.

Starting with:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

If you know the desired frequency and inductance, capacitance can be calculated as:$$C = \frac{1}{(2\pi f_0)^2L}$$

If you know the desired frequency and capacitance, inductance can be calculated as:$$L = \frac{1}{(2\pi f_0)^2C}$$

These equations are useful for component selection.

Although the calculator accepts L and C as inputs rather than directly solving for an unknown component, understanding these rearrangements helps explain how LC circuits are designed around a target frequency.

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Practical Tips for Using the LC Circuit Calculator

Check Your Units

The most common source of errors is using the wrong unit multiplier. Always confirm whether the component value is in H, mH, µH, F, mF, µF, or nF.

Use the Component's Actual Rated Value

For an initial estimate, the nominal component value is appropriate. For precision applications, consider the actual measured value and tolerance.

Avoid Entering Zero

Both inductance and capacitance must be greater than zero. A zero value cannot produce a meaningful LC resonant frequency using the standard equation.

Pay Attention to Scientific Notation

Very small inductances and capacitances can result in high frequencies. The calculator uses scientific notation for the frequency-related outputs, making very large or small numbers easier to read.

Compare Reactances

At ideal resonance, the inductive and capacitive reactances should be equal in magnitude. Comparing these two calculator outputs provides a useful check on the calculation.

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Advantages of Using an LC Circuit Calculator

Manual calculations are useful for learning, but an online calculator can make repeated calculations much faster.

The calculator can:

• Reduce repetitive mathematical work
• Handle unit conversions
• Calculate resonant frequency automatically
• Calculate angular frequency
• Determine inductive reactance
• Determine capacitive reactance
• Support common electronic component units
• Make component comparisons easier
• Provide quick preliminary design estimates

For students, electronics hobbyists, technicians, and engineers, this can be a convenient first step when analyzing an LC resonant network.

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Frequently Asked Questions

1. What is an LC Circuit Calculator?

An LC Circuit Calculator is a tool used to determine the resonant frequency and related characteristics of an ideal LC circuit from its inductance and capacitance values.

2. What formula is used for LC resonant frequency?

The standard formula is:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

where L is inductance in henries and C is capacitance in farads.

3. What is the resonant angular frequency of an LC circuit?

The resonant angular frequency is:$$\omega_0 = \frac{1}{\sqrt{LC}}$$

It is measured in radians per second.

4. What units can I use for inductance?

The calculator supports H, mH, and µH. It converts the selected value to henries before calculating the resonance.

5. What capacitance units does the calculator support?

You can enter capacitance in F, mF, µF, or nF. The calculator converts the selected value to farads for the calculation.

6. What is inductive reactance?

Inductive reactance is the opposition an inductor presents to alternating current. It is calculated using:$$X_L = 2\pi fL$$

and is measured in ohms.

7. What is capacitive reactance?

Capacitive reactance describes the opposition a capacitor presents to alternating current. It is calculated using:$$X_C = \frac{1}{2\pi fC}$$

and is measured in ohms.

8. Are inductive and capacitive reactances equal at resonance?

In an ideal LC circuit at resonance, the magnitudes of inductive and capacitive reactance are equal:$$X_L = X_C$$

Their reactive effects oppose each other.

9. Does increasing capacitance increase resonant frequency?

No. With inductance held constant, increasing capacitance decreases resonant frequency. Decreasing capacitance increases resonant frequency.

10. Can this calculator predict the exact resonance of a physical circuit?

It calculates the ideal theoretical resonance from the supplied L and C values. Real components have resistance, tolerances, parasitic effects, and losses, so measured resonance can differ from the theoretical result.

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Conclusion

The LC Circuit Calculator provides a convenient way to analyze the fundamental frequency characteristics of an ideal inductor-capacitor circuit. By entering the inductance and capacitance, you can quickly determine the circuit's resonant frequency, angular frequency, inductive reactance, and capacitive reactance.

The key equation is:$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

This equation demonstrates why both components matter. Increasing either inductance or capacitance lowers the resonant frequency, while reducing either value raises it.

The calculator also handles common units such as henries, millihenries, microhenries, farads, millifarads, microfarads, and nanofarads, reducing the need for manual unit conversion. The additional reactance results help explain what happens at resonance, where the inductive and capacitive reactances have equal magnitude in the ideal case.

LC circuits have applications in tuning systems, filters, oscillators, impedance matching, radio-frequency electronics, and signal-processing circuits. For basic analysis and preliminary component selection, the standard LC formulas provide a useful starting point.

However, practical circuits are affected by component tolerances, resistance, parasitic capacitance and inductance, ESR, and other non-ideal characteristics. Therefore, theoretical calculations should be supplemented with component specifications and measurements when designing precise or high-frequency circuits.

Whether you are learning electronics, checking a homework calculation, selecting components, or exploring how inductance and capacitance influence resonance, this LC Circuit Calculator can provide a fast and convenient way to understand the relationship between L, C, and resonant frequency.
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