What is the LC resonance formula?

The resonant frequency is f0 = 1 / (2π√LC), where L is inductance in henries and C is capacitance in farads.

Does the same formula work for series and parallel LC circuits?

Yes. The ideal resonant frequency formula is the same, but series resonance gives minimum impedance while parallel resonance gives maximum impedance.

Why is my measured resonance different from calculated resonance?

Real components have tolerance, ESR, coil resistance, stray capacitance and PCB layout effects that can shift the measured resonance from the ideal calculation.

What does Q factor mean in an LC circuit?

Q factor describes how sharp or selective the resonance is. Higher Q means lower loss and narrower bandwidth; lower Q means more damping and wider bandwidth.

LC Resonance Calculator — Resonant Frequency, L, C, Q & Bandwidth

Q: What is LC resonance?

LC resonance occurs when an inductor and capacitor exchange energy at a natural frequency where inductive reactance equals capacitive reactance.

LC Resonance Calculator

Calculate resonant frequency, required inductor value, required capacitor value, Q factor, bandwidth and reactance for LC tank circuits.

🎯 Key Insight: An LC circuit resonates when XL = XC. At this frequency, the inductor and capacitor exchange stored energy, making the circuit useful for RF tuning, oscillators, filters and tank circuits.

〰️ LC Tank — Resonance Point

Inductance

Capacitance

Resistance / ESR (optional)

Presets:10mH + 100nF100µH + 100nFRF tankCrossover

Resonant Frequency

—

XL = XC

🎯 At resonance: Inductive reactance equals capacitive reactance. In a series LC/RLC circuit, the reactive part cancels.

XL at f₀

—

same as XC

XC at f₀

—

same as XL

Angular Frequency

—

ω₀ = 2πf₀

Q Factor

—

if R entered

Bandwidth

—

f₀ / Q

Formula

1/(2π√LC)

resonance

———

Target Frequency

Capacitance

Presets:100kHz + 100nF455kHz IF1MHz + 220pF13.56MHz RFID

Required Inductance

—

Solve L

Frequency

—

target f₀

Capacitance

—

given C

Reactance at f₀

—

XL = XC

Formula

1/((2πf)²C)

solve for L

———

Target Frequency

Inductance

Presets:100kHz + 100µH455kHz IF1MHz + 100µH13.56MHz + 1µH

Required Capacitance

—

Solve C

Frequency

—

target f₀

Inductance

—

given L

Reactance at f₀

—

XL = XC

Formula

1/((2πf)²L)

solve for C

———

Inductance

Capacitance

Series Resistance / ESR

Presets:100µH + 100nFRF tankAudio LCCrossover

Q Factor

—

Resonant Frequency

—

f₀

Bandwidth

—

f₀ / Q

XL = XC

—

at f₀

Lower -3dB

—

approx

Upper -3dB

—

approx

Series R

—

ESR / winding R

———

📐 LC Resonance Formulas

Frequency

f₀ = 1/(2π√LC)
ω₀ = 2πf₀
XL = XC at f₀

Find L

L = 1 / ((2πf)²C)
XL = 2πfL
Unit: henry

Find C

C = 1 / ((2πf)²L)
XC = 1/(2πfC)
Unit: farad

Q & BW

Q = XL / R
BW = f₀ / Q
f₁/f₂ ≈ f₀ ± BW/2

📋 Quick Reference

🎯 Common LC Pairs

10 mH + 100 nF5.03 kHz

100 µH + 100 nF50.3 kHz

47 µH + 22 pF4.95 MHz

1 µH + 100 pF15.9 MHz

🔵 Typical Uses

Audio filtersHz–kHz

SMPS tankskHz

AM/RF tuningkHz–MHz

RFID/NFC13.56 MHz

🟠 Practical Notes

Higher Llower f₀

Higher Clower f₀

Higher Rlower Q

High Qnarrow BW

📚 Engineering Notes

Series vs parallel LCThe same resonant frequency formula applies, but impedance behavior is different. Series resonance gives minimum impedance; parallel resonance gives maximum impedance.

Real parts shift resultsCoil resistance, capacitor ESR, tolerance, stray capacitance and PCB layout can shift the measured resonance from the ideal calculation.

Q factor controls selectivityHigher Q means a sharper resonance peak and narrower bandwidth. Lower Q means wider response and more damping.

Use correct unitsThe formula needs L in henries and C in farads. This calculator converts µH, mH, pF, nF and µF automatically.

What is LC Resonance?

LC resonance is the natural frequency of an inductor-capacitor circuit. At resonance, the energy stored in the magnetic field of the inductor and the electric field of the capacitor transfers back and forth.

LC Resonant Frequency Formula

The standard formula is f₀ = 1/(2π√LC). Increasing either inductance or capacitance lowers the resonant frequency. Decreasing either value raises the resonant frequency.

❓ Frequently Asked Questions

The result is in hertz (Hz). The calculator automatically formats it as Hz, kHz or MHz depending on the value.

Yes, the ideal resonant frequency formula is the same. The circuit behavior is different: series LC has low impedance at resonance, while parallel LC has high impedance at resonance.

Real components have tolerance, ESR, coil resistance, parasitic capacitance and layout effects. These practical factors can move the actual resonance slightly.

High Q means low loss and a narrow bandwidth around resonance. It is useful in tuned circuits but may be too sharp for wider filters.

Yes, it is useful as a starting point for RF tanks, oscillators and antenna matching networks. At high frequency, include stray capacitance, coil self-capacitance, PCB layout and component tolerance in the final design.

💡 Rule of Thumb: Doubling L or C does not halve the resonance frequency. Because of the square root, doubling L or C reduces f₀ by about 29.3%.