An LC resonant frequency calculator is a useful tool for determining the natural resonant frequency of an LC circuit from two fundamental components: inductance (L) and capacitance (C). LC circuits are widely used in electronics for tuning, filtering, oscillation, signal selection, impedance matching, and many other applications.

An LC circuit contains an inductor and a capacitor that exchange energy. The capacitor stores energy in an electric field, while the inductor stores energy in a magnetic field. Under ideal conditions, energy moves back and forth between these two components at a characteristic frequency called the resonant frequency.

Calculating this frequency manually is straightforward when the inductance and capacitance are already expressed in compatible SI units. However, electronic components are commonly specified using values such as microhenries (µH), nanohenries (nH), picofarads (pF), microfarads (µF), and nanofarads (nF). Converting these values correctly before applying the formula can be tedious and can introduce errors.

This LC Resonant Frequency Calculator simplifies the process. Enter the inductance and capacitance, select their respective units, and the calculator determines the resonant frequency. The result is displayed in hertz (Hz), kilohertz (kHz), and megahertz (MHz), along with the circuit's angular frequency in radians per second (rad/s).

This guide explains how the calculator works, the LC resonance formula, unit conversions, practical examples, important concepts, applications, and common questions.

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What Is an LC Circuit?

An LC circuit is an electrical circuit consisting primarily of an inductor (L) and a capacitor (C).

The inductor resists changes in current and stores energy magnetically. The capacitor stores electrical energy and resists changes in voltage. When these components are connected together, they can exchange stored energy.

In an ideal LC circuit:

1. The capacitor initially stores electrical energy.
2. The capacitor releases energy into the inductor.
3. The inductor stores the energy in its magnetic field.
4. The magnetic field collapses and sends energy back toward the capacitor.
5. The process repeats.

This continuous exchange creates an oscillation with a characteristic frequency.

That frequency is known as the LC resonant frequency or natural frequency.

The resonant frequency is determined primarily by the values of the inductance and capacitance.

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What Is LC Resonance?

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

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

Where:

• $f_0$ = resonant frequency in hertz (Hz)
• $L$ = inductance in henries (H)
• $C$ = capacitance in farads (F)
• $\pi$ ≈ 3.14159

The calculator uses this fundamental relationship to determine the resonant frequency.

Because both L and C appear inside a square root, changing either component affects the resonant frequency in a predictable way.

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LC Resonant Frequency Formula Explained

The primary formula is:

f = 1 / (2π√(LC))

The calculation happens in several stages.

Step 1: Convert Inductance to Henries

The inductance must be converted to henries.

For example:

1 mH = 0.001 H

1 µH = 0.000001 H

1 nH = 0.000000001 H

Step 2: Convert Capacitance to Farads

Capacitance must be converted to farads.

For example:

1 mF = 0.001 F

1 µF = 0.000001 F

1 nF = 0.000000001 F

1 pF = 0.000000000001 F

Step 3: Multiply L and C

Calculate:$$LC$$

Step 4: Take the Square Root

Calculate:$$\sqrt{LC}$$

Step 5: Multiply by 2π

Calculate:$$2\pi\sqrt{LC}$$

Step 6: Divide 1 by the Result

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

The result is the resonant frequency in hertz.

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Angular Frequency Formula

The calculator also provides angular frequency, represented by the Greek letter omega:$$\omega_0 = \frac{1}{\sqrt{LC}}$$

Angular frequency is measured in radians per second (rad/s).

The relationship between angular frequency and ordinary frequency is:$$\omega_0 = 2\pi f_0$$

Therefore:$$f_0 = \frac{\omega_0}{2\pi}$$

The calculator first determines angular frequency from L and C and then converts it into ordinary frequency in hertz.

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How to Use the LC Resonant Frequency Calculator

Using the calculator is simple because it handles the necessary unit conversions automatically.

Step 1: Enter the Inductance

Enter the value of your inductor.

For example:

10

Then choose the appropriate unit, such as:

µH

This represents 10 microhenries.

The calculator supports:

• H
• mH
• µH
• nH

Step 2: Enter the Capacitance

Enter the capacitor value.

For example:

100

Then select:

pF

This represents 100 picofarads.

The calculator supports:

• F
• mF
• µF
• nF
• pF

Step 3: Click Calculate

Press the Calculate button.

The calculator converts both component values into their base SI units and applies the LC resonant frequency formula.

Step 4: Review the Results

The calculator provides:

• Resonant frequency in Hz
• Resonant frequency in kHz
• Resonant frequency in MHz
• Angular frequency in rad/s

This makes it convenient to interpret the result regardless of the frequency range.

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Supported Inductance Units

The calculator supports four inductance units.

Unit	Symbol	Equivalent in Henries
Henry	H	1 H
Millihenry	mH	0.001 H
Microhenry	µH	0.000001 H
Nanohenry	nH	0.000000001 H

For electronic circuits, microhenries and nanohenries are particularly common in high-frequency applications.

For example:

25 µH = 25 × 10⁻⁶ H

and:

50 nH = 50 × 10⁻⁹ H

Correct unit conversion is essential because the resonance formula expects inductance in henries.

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Supported Capacitance Units

The calculator supports five capacitance units.

Unit	Symbol	Equivalent in Farads
Farad	F	1 F
Millifarad	mF	0.001 F
Microfarad	µF	0.000001 F
Nanofarad	nF	0.000000001 F
Picofarad	pF	0.000000000001 F

Many practical electronic circuits use µF, nF, or pF capacitors.

For example:

10 nF = 10 × 10⁻⁹ F

while:

100 pF = 100 × 10⁻¹² F

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Worked Example 1: 10 µH and 100 pF

Suppose an LC circuit has:

• Inductance = 10 µH
• Capacitance = 100 pF

Convert the values to SI units:$$L=10\times10^{-6}H$$$$C=100\times10^{-12}F$$

Therefore:$$L=1\times10^{-5}H$$

and:$$C=1\times10^{-10}F$$

Now multiply:$$LC=(1\times10^{-5})(1\times10^{-10})$$$$LC=1\times10^{-15}$$

Take the square root:$$\sqrt{LC}\approx3.1623\times10^{-8}$$

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

The resulting resonant frequency is approximately:

5.03 MHz

So an ideal LC circuit using a 10 µH inductor and 100 pF capacitor has a resonant frequency of roughly 5.03 MHz.

The calculator also provides the corresponding value in hertz and kilohertz.

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Worked Example 2: 1 mH and 1 µF

Consider:

• Inductance = 1 mH
• Capacitance = 1 µF

Convert:$$L=0.001H$$$$C=0.000001F$$

Then:$$LC=10^{-9}$$

The resonant frequency is:$$f_0=\frac{1}{2\pi\sqrt{10^{-9}}}$$

The result is approximately:

5.03 kHz

This illustrates how larger inductance and capacitance values generally produce a lower resonant frequency.

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Worked Example 3: 100 µH and 10 nF

Suppose:

• L = 100 µH
• C = 10 nF

Convert:$$L=100\times10^{-6}=1\times10^{-4}H$$$$C=10\times10^{-9}=1\times10^{-8}F$$

The resulting resonant frequency is approximately:

159.15 kHz

This type of frequency range is useful for understanding how component combinations determine the operating frequency of an LC network.

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How Inductance Affects Resonant Frequency

The relationship between inductance and resonant frequency is inverse-square-root based.

The formula is:$$f_0\propto\frac{1}{\sqrt{L}}$$

This means increasing inductance decreases the resonant frequency.

For example, if capacitance remains constant and inductance increases by a factor of 4:$$L_{new}=4L$$

Then:$$f_{new}=\frac{f_{old}}{2}$$

So quadrupling the inductance cuts the resonant frequency in half.

Conversely, reducing the inductance increases the resonant frequency.

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How Capacitance Affects Resonant Frequency

Capacitance has a similar relationship:$$f_0\propto\frac{1}{\sqrt{C}}$$

Increasing capacitance lowers the resonant frequency.

If capacitance increases by a factor of 4:$$C_{new}=4C$$

the resonant frequency becomes half the original value.

Likewise, reducing capacitance increases the resonant frequency.

This principle is particularly important in tuning circuits because changing capacitance can provide a convenient way to adjust the resonant frequency.

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Effect of Changing L and C

The following table illustrates the general relationship between component changes and resonant frequency.

Change	Effect on Resonant Frequency
Increase L	Frequency decreases
Decrease L	Frequency increases
Increase C	Frequency decreases
Decrease C	Frequency increases
Increase L by 4×	Frequency decreases by 2×
Increase C by 4×	Frequency decreases by 2×
Decrease L by 4×	Frequency increases by 2×
Decrease C by 4×	Frequency increases by 2×

This inverse-square-root relationship is one of the most important characteristics of an LC resonant circuit.

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LC Resonant Frequency Conversion Table

The calculator displays the same frequency in three common units.

Frequency in Hz	Frequency in kHz	Frequency in MHz
1,000 Hz	1 kHz	0.001 MHz
10,000 Hz	10 kHz	0.01 MHz
100,000 Hz	100 kHz	0.1 MHz
1,000,000 Hz	1,000 kHz	1 MHz
5,000,000 Hz	5,000 kHz	5 MHz
10,000,000 Hz	10,000 kHz	10 MHz
100,000,000 Hz	100,000 kHz	100 MHz

Remember:

1 kHz = 1,000 Hz

and:

1 MHz = 1,000,000 Hz

The calculator automatically provides these conversions so you do not have to perform them manually.

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Why Unit Selection Is Important

Component values can look deceptively similar when their prefixes are overlooked.

For example:

1 µH is not the same as 1 mH.

Similarly:

1 nF is not the same as 1 pF.

The prefixes represent powers of ten:

• milli = 10⁻³
• micro = 10⁻⁶
• nano = 10⁻⁹
• pico = 10⁻¹²

Because inductance and capacitance appear inside a square root, a unit error can produce a substantial difference in the final frequency.

Always select the unit that corresponds exactly to the component value.

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Common Applications of LC Resonant Circuits

LC circuits are fundamental components of many electronic systems.

Radio Tuning

LC networks can be used to select a particular frequency from a range of radio signals. Variable capacitors can change the resonant frequency and allow a receiver to tune between stations.

Oscillators

LC networks are commonly used as frequency-determining elements in oscillator circuits.

Filters

LC circuits can be used to create frequency-selective networks that pass or reject particular frequency ranges.

Impedance Matching

LC matching networks can help transform one impedance into another, improving power transfer between circuit stages.

RF Electronics

Radio-frequency circuits frequently use small inductors and capacitors to achieve resonance at high frequencies.

Antenna Networks

LC matching and tuning networks are often used with antennas to help achieve desirable electrical characteristics at a target frequency.

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Ideal Resonance vs. Real-World LC Circuits

The formula used by the calculator assumes an ideal LC circuit.

Real components are not perfect.

An actual inductor has resistance, parasitic capacitance, and other non-ideal characteristics. A real capacitor also has equivalent series resistance, inductance, leakage, and dielectric-related characteristics.

These properties can cause the actual resonant frequency to differ slightly from the theoretical result.

Other factors can include:

• Component tolerances
• Temperature changes
• PCB parasitics
• Wiring inductance
• Stray capacitance
• Inductor self-resonance
• Capacitor equivalent series resistance
• Measurement equipment loading

Therefore, the calculator should be viewed as a theoretical or nominal resonance calculator, rather than a replacement for detailed circuit simulation or measurement.

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What Is the Difference Between Resonant Frequency and Angular Frequency?

Although they describe the same oscillatory behavior, frequency and angular frequency use different units.

Frequency

Frequency is measured in hertz (Hz) and represents cycles per second.

For example:

1,000 Hz = 1,000 cycles per second

Angular Frequency

Angular frequency is measured in radians per second (rad/s).

The relationship is:$$\omega=2\pi f$$

Therefore, angular frequency is approximately 6.283 times the ordinary frequency.

For example, if:$$f=1000Hz$$

then:$$\omega\approx6283.19rad/s$$

The calculator provides both values to make the result useful for different types of electronics calculations.

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LC Resonance vs. RLC Resonance

An LC circuit contains an inductor and capacitor, while an RLC circuit also includes resistance.

Resistance changes the behavior of the circuit by introducing energy loss and affecting the sharpness of resonance.

An ideal LC circuit is useful for determining the basic natural frequency:$$f_0=\frac{1}{2\pi\sqrt{LC}}$$

In practical circuits, resistance and component losses can affect the observed response.

Therefore, the LC calculator is best suited to determining the theoretical resonant frequency based specifically on L and C values.

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Tips for Using the Calculator Accurately

Check the Component Datasheets

Use the actual nominal inductance and capacitance values from the component specifications.

Verify Prefixes

Make sure you distinguish between mH, µH, nH and between µF, nF, and pF.

Use Positive Values

Inductance and capacitance values entered into this calculator must be greater than zero.

Consider Component Tolerance

A capacitor labeled with a nominal value may not have exactly that value in practice. The same applies to inductors.

Consider Parasitic Effects

At higher frequencies, PCB traces, component leads, package characteristics, and stray capacitance can influence the actual circuit.

Use Appropriate Precision

The calculator presents the results in a practical numerical format. Extremely precise calculator results should not be interpreted as indicating equivalent physical precision in real-world components.

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Quick Reference: LC Resonant Frequency Equations

For convenience, the main equations are:

Resonant Frequency

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

Angular Frequency

$$\boxed{\omega_0=\frac{1}{\sqrt{LC}}}$$

Frequency From Angular Frequency

$$\boxed{f_0=\frac{\omega_0}{2\pi}}$$

Where:

• f₀ = resonant frequency in Hz
• ω₀ = angular frequency in rad/s
• L = inductance in H
• C = capacitance in F

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Frequently Asked Questions

1. What does an LC Resonant Frequency Calculator calculate?

It calculates the theoretical resonant frequency of an LC circuit using the inductance and capacitance values. The result is provided in Hz, kHz, and MHz, along with angular frequency in rad/s.

2. What is the formula for LC resonant frequency?

The standard ideal LC resonance formula is:

f = 1 / (2π√LC)

Inductance must be expressed in henries and capacitance in farads when using the formula directly.

3. What units can I enter for inductance?

The calculator supports H, mH, µH, and nH. It automatically converts the selected value to henries for the calculation.

4. What units can I enter for capacitance?

You can enter capacitance in F, mF, µF, nF, or pF. The calculator converts the selected value into farads automatically.

5. What happens if I increase the inductance?

Increasing inductance lowers the LC resonant frequency when capacitance remains unchanged. The relationship follows an inverse square-root dependence.

6. What happens if I increase the capacitance?

Increasing capacitance also lowers the resonant frequency when inductance remains unchanged. Reducing capacitance increases the resonant frequency.

7. What is angular frequency in an LC circuit?

Angular frequency is the resonant frequency expressed in radians per second. It is calculated using:

ω = 1 / √LC

It is related to ordinary frequency by ω = 2πf.

8. Is the calculator accurate for real-world circuits?

It provides the theoretical resonant frequency based on the specified L and C values. Real circuits can differ because of component tolerances, resistance, parasitic capacitance, parasitic inductance, temperature, and other non-ideal effects.

9. Can this calculator be used for RF circuits?

Yes. It can calculate the theoretical LC resonance for RF circuits using appropriate inductance and capacitance values. However, at high frequencies, parasitic effects and component self-resonance can become significant.

10. Why does my measured resonant frequency differ from the calculator result?

The calculator uses nominal L and C values and an ideal LC model. Actual components have tolerances and parasitic characteristics, while circuit boards and measurement equipment can introduce additional capacitance, inductance, resistance, and loading.

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Conclusion

The LC Resonant Frequency Calculator provides a convenient way to determine the theoretical resonant frequency of an LC circuit from its inductance and capacitance values. Instead of manually converting component prefixes and working through several mathematical steps, you can enter the values directly using common units such as H, mH, µH, nH, F, mF, µF, nF, and pF.

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

The calculator also determines angular frequency using:$$\omega_0=\frac{1}{\sqrt{LC}}$$

Understanding these equations makes it easier to predict how an LC circuit will respond when component values change. Increasing either inductance or capacitance lowers the resonant frequency, while decreasing either value raises it.

LC resonance is fundamental to numerous electronic applications, including radio tuning, oscillators, filters, RF circuits, antenna matching, and impedance-matching networks. The calculator can therefore be useful for students, electronics hobbyists, engineers, technicians, and anyone learning about resonant circuits.

For the most reliable practical results, remember that real inductors and capacitors are not ideal. Component tolerances, parasitic elements, temperature, PCB layout, and measurement conditions can all influence the actual resonant frequency. Use the calculator as a fast theoretical estimate, and use component specifications, circuit simulation, or measurement when greater real-world accuracy is required.
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