LC Resonance Calculator

Q: What is the resonant frequency of a 100 µH coil and a 100 pF capacitor?

About 1.59 MHz . Work it out step by step: L × C = (100 × 10⁻⁶ H) × (100 × 10⁻¹² F) = 1 × 10⁻¹⁴ √(1 × 10⁻¹⁴) = 1 × 10⁻⁷ f = 1 ÷ (2π × 1 × 10⁻⁷) = 1,591,500 Hz That is 1.5915 MHz, which sits in the AM radio band.

Q: What happens to the resonant frequency if you double the capacitance?

The frequency drops to about 71% of what it was , so it falls by roughly 29%. Frequency depends on the square root of L × C. Doubling C means dividing the frequency by √2 (about 1.414). Doubling the inductance does the same thing. To cut the frequency in half, you need four times the capacitance or four times the inductance.

Q: Do series and parallel LC circuits have the same resonant frequency?

Yes. Both use f = 1 / (2π√(LC)) , so the same L and C give the same frequency either way. What changes is the behavior at that frequency: Series LC: impedance drops near zero, so current is highest. It acts like a short for that one frequency. Parallel LC: impedance goes very high, so current from the source is lowest. It acts like a block for that one frequency.

LC Resonance Calculator

Updated Sep 3, 2026 By Jehan Wadia

Introduction

An LC circuit is a coil (inductor) and a capacitor joined together. At one special frequency, the coil and the capacitor push back on the current by the same amount. That frequency is called the resonant frequency. Radios, filters, and tuners all use this idea to pick out one signal and ignore the rest.

This LC resonance calculator finds that frequency. Pick what you want to solve for, frequency (f), inductance (L), or capacitance (C), then type in the other two values. Click a label on the circuit picture or use the buttons. You can enter values in units you already use, like nH, µH, pF, nF, kHz, MHz, or GHz.

The tool uses the standard formula:

f = 1 / (2π√(LC))

You also get three more numbers: the characteristic impedance (Z₀), the angular frequency (ω₀), and the period (T). A step-by-step solution shows the math, so you can check your own work or study how it is done. The chart shows how the coil's reactance and the capacitor's reactance change with frequency, and where they cross at resonance.

Use it to design a tank circuit, plan a filter, tune an antenna, or finish a physics homework problem.

How to use our LC Resonance Calculator

Pick which value you want to find, type in the other two circuit values, and the calculator gives you the resonant frequency, inductance, or capacitance, plus the characteristic impedance, angular frequency, and period.

Solve for: Choose f, L, or C. You can click the letter on the circuit diagram or pick a radio button. The one you choose turns into the answer box, so you do not type in it.

Frequency (f): Type the resonant frequency of the LC circuit and pick its unit: Hz, kHz, MHz, or GHz. Leave this blank if you are solving for frequency.

Inductance (L): Type the total coil inductance and pick its unit: H, mH, µH, or nH. Leave this blank if you are solving for inductance.

Capacitance (C): Type the total tank capacitance and pick its unit: µF, nF, or pF. Leave this blank if you are solving for capacitance.

Characteristic Impedance (Z₀) unit: In the results, pick mΩ, Ω, kΩ, or MΩ to change how the impedance and the chart are shown.

Calculate: Click Calculate to see the answer, the step-by-step math, and a chart of reactance versus frequency. Click Reset to start over with the sample values.

What Is LC Resonance?

An LC circuit is a loop with two parts: a coil (inductor, L) and a capacitor (C). The capacitor stores energy in an electric field. The coil stores energy in a magnetic field. In an LC loop, energy moves back and forth between the two, over and over. This swapping makes the current and voltage swing like a wave.

There is one special speed for this swing. It is called the resonant frequency. At that frequency the coil's push and the capacitor's push cancel each other out. The circuit lets that one frequency pass easily and blocks others. That is why LC circuits are also called tuned circuits or tank circuits.

The Resonant Frequency Formula

The resonant frequency of an LC circuit is:

f = 1 / (2π√(LC))

Here f is in hertz (Hz), L is in henries (H), and C is in farads (F). You can flip the formula around to find L or C instead:

L = 1 / (4π²f²C)
C = 1 / (4π²f²L)

Bigger parts mean a slower wave. If you make L or C larger, the frequency drops. If you make them smaller, the frequency goes up. Because of the square root, making C four times bigger cuts the frequency in half.

Reactance: Why Resonance Happens

Reactance is how much a part fights changing current. It changes with frequency:

Inductive reactance: X_L = 2πfL, which grows as frequency goes up.
Capacitive reactance: X_C = 1 / (2πfC), which shrinks as frequency goes up.

Resonance is the point where these two lines cross, so X_L = X_C. In a series LC circuit, the total reactance drops to almost zero there, so current is largest. In a parallel LC circuit, the opposite happens: the circuit acts like a very high resistance at resonance.

Other Handy Values

Angular frequency: ω₀ = 2πf, measured in radians per second.
Period: T = 1/f, the time for one full swing.
Characteristic impedance: Z₀ = √(L/C). This is the reactance of each part at resonance. It tells you how "stiff" the tank is and helps you pick parts that match the rest of your circuit.

Where LC Circuits Are Used

Tuned LC circuits show up almost everywhere signals are used:

Radio and TV tuners that pick one station out of many
Filters that pass or block certain frequencies
Oscillators and clock circuits
Antenna matching networks
Wireless chargers and RFID tags
Power supplies, to smooth out noise

Real Circuits Have Losses

The formula above assumes a perfect circuit with no resistance. Real coils and wires do have some resistance, so the wave slowly fades unless energy is added. Resistance also widens the resonance, meaning nearby frequencies get through too. Engineers measure this with the Q factor (quality factor). A high Q means a sharp, narrow peak and a very selective circuit. A low Q means a broad, gentle peak. Stray capacitance in wires and boards can also shift the real frequency a little, so tuned circuits often use a trimmer capacitor for fine adjustment.

Formulas used

Resonant frequency

f = \frac{1}{2\pi\sqrt{LC}}

Inductance at resonance

L = \frac{1}{4\pi^2 f^2 C}

Capacitance at resonance

C = \frac{1}{4\pi^2 f^2 L}

Characteristic impedance

Z_0 = \sqrt{\frac{L}{C}}

Angular resonant frequency

\omega_0 = 2\pi f

Period at resonance

T = \frac{1}{f}

Inductive and capacitive reactance vs. frequency

X_L = 2\pi f L, \qquad X_C = \frac{1}{2\pi f C}

Net reactance magnitude

|X| = \left| X_L - X_C \right|

Frequently asked questions

What is the resonant frequency of a 100 µH coil and a 100 pF capacitor?

About 1.59 MHz.

Work it out step by step:

L × C = (100 × 10⁻⁶ H) × (100 × 10⁻¹² F) = 1 × 10⁻¹⁴
√(1 × 10⁻¹⁴) = 1 × 10⁻⁷
f = 1 ÷ (2π × 1 × 10⁻⁷) = 1,591,500 Hz

That is 1.5915 MHz, which sits in the AM radio band.

What happens to the resonant frequency if you double the capacitance?

The frequency drops to about 71% of what it was, so it falls by roughly 29%.

Frequency depends on the square root of L × C. Doubling C means dividing the frequency by √2 (about 1.414). Doubling the inductance does the same thing. To cut the frequency in half, you need four times the capacitance or four times the inductance.

Do series and parallel LC circuits have the same resonant frequency?

Yes. Both use f = 1 / (2π√(LC)), so the same L and C give the same frequency either way.

What changes is the behavior at that frequency:

Series LC: impedance drops near zero, so current is highest. It acts like a short for that one frequency.
Parallel LC: impedance goes very high, so current from the source is lowest. It acts like a block for that one frequency.

How do you pick L and C values for a target frequency?

Many L and C pairs give the same frequency, so pick the pair using the characteristic impedance Z₀ = √(L/C). For RF work, Z₀ of 50 Ω to 500 Ω is common.

Then:

L = Z₀ / (2πf)
C = 1 / (2πf × Z₀)

Example: for 10 MHz with Z₀ = 300 Ω, L ≈ 4.8 µH and C ≈ 53 pF.

How do you calculate the Q factor of an LC circuit?

Q compares the stored energy to the energy lost each cycle. Use the coil and wire resistance R:

Series LC: Q = √(L/C) ÷ R, which is Z₀ ÷ R
Parallel LC: Q = R ÷ √(L/C)

Bandwidth is then BW = f₀ ÷ Q. So a 10 MHz circuit with Q = 100 passes a band about 100 kHz wide. Higher Q means a sharper, more selective peak.

What is the self-resonant frequency of an inductor?

Every coil has a small amount of stray capacitance between its turns. That stray capacitance resonates with the coil's own inductance at a frequency called the self-resonant frequency (SRF).

Below the SRF the part acts like an inductor. Above it, the part acts more like a capacitor. Keep your working frequency well under the SRF listed on the data sheet, usually below about one third of it.

Does resistance change the resonant frequency of an LC circuit?

Only a little, and often not enough to notice. In a series circuit, the current still peaks at f = 1 / (2π√(LC)).

Resistance does two other things. It makes the peak wider and lower, so the circuit is less selective. And if you ring the circuit with a pulse, heavy resistance makes the ringing die out fast and slightly slows it down.

How much does capacitor tolerance shift the resonant frequency?

About half as much as the part error, because of the square root.

A 10% capacitance error shifts the frequency about 5%
A 20% error shifts it about 10%

If both L and C are off, the errors add. That is why tuned circuits often use a trimmer capacitor or an adjustable core so you can set the exact frequency by hand.

Does adding capacitors in parallel raise or lower the resonant frequency?

It lowers the frequency. Capacitors in parallel add together, so total C goes up.

Two 100 pF caps in parallel act like 200 pF, which drops the frequency to about 71% of its old value. Capacitors in series give less total capacitance, so they raise the frequency. Inductors work the opposite way: series adds, parallel subtracts.

Why is it called a tank circuit?

Because it holds energy like a water tank. The capacitor fills with charge, then dumps it into the coil as a magnetic field, then the coil pushes it back into the capacitor.

This back-and-forth keeps going at the resonant frequency. In a perfect circuit it would never stop. In real circuits, wire resistance drains the energy, so the swings fade unless a small push is added each cycle.

How do you convert inductance and capacitance units for the resonance formula?

The formula needs henries and farads, so convert first:

1 H = 1,000 mH = 1,000,000 µH = 1,000,000,000 nH
1 µF = 1,000 nF = 1,000,000 pF
1 mH = 10⁻³ H, 1 µH = 10⁻⁶ H, 1 nH = 10⁻⁹ H
1 µF = 10⁻⁶ F, 1 nF = 10⁻⁹ F, 1 pF = 10⁻¹² F

Mixing up nH and µH is the most common mistake, and it moves the answer by a factor of about 32.

Does voltage or current change the resonant frequency?

No. Only L and C set the frequency. A bigger signal makes the swings larger, not faster.

One exception: coils with iron or ferrite cores can saturate at high current, which lowers their inductance and raises the frequency. Some capacitors, like class II ceramics, also lose capacitance under high DC voltage, which shifts the frequency up.

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