Resonant Frequency Calculator (LC Circuit)
Find the resonant frequency of an LC circuit, or solve for the inductance or capacitance needed to hit a target frequency.
🔁 What is Resonant Frequency in an LC Circuit?
The resonant frequency of an LC circuit is the specific frequency at which an inductor and a capacitor exchange energy back and forth with maximum efficiency, causing the circuit's reactance to peak or cancel depending on the configuration. At this frequency, given by Thomson's formula f0 = 1/(2*pi*sqrt(LC)), the inductive and capacitive reactances are equal in magnitude, and the circuit's behaviour is dominated purely by this energy exchange rather than by either component alone.
LC resonance is the foundation of tuned circuits everywhere. Radio and television tuners use a variable LC circuit to select one broadcast frequency out of the many present in the air. Oscillator circuits use LC resonance to set a stable output frequency in everything from function generators to RF transmitters. Filter designers use it to build band-pass and band-stop filters that pass or reject a narrow range of frequencies, and wireless power and RFID systems tune their coils to resonate at the frequency they need to couple energy efficiently.
A common misconception is that resonant frequency depends on resistance. It does not, an ideal LC circuit's resonant frequency is set entirely by L and C. Resistance in a real circuit affects how sharp or damped the resonance peak is (its quality factor), but not where the peak sits on the frequency axis. Another common mix-up is between resonant frequency (in hertz, cycles per second) and angular resonant frequency (in radians per second): they describe the same physical resonance, just in different units, related by omega0 = 2*pi*f0.
This calculator lets you go in any of the three useful directions: find the resonant frequency from known L and C, find the inductance needed to hit a target frequency with a known capacitor, or find the capacitance needed to hit a target frequency with a known inductor.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Resonant Frequency From L and C
L = 100 mH, C = 1 µF, find f₀
Example 2 — AM Radio Tuning Circuit
L = 200 µH (0.2 mH), C = 300 pF (0.0003 µF), find f₀
Example 3 — Solving for L (Round-Trip Check)
Target f₀ = 503.29 Hz, C = 1 µF, find L
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for LC circuit resonant frequency?
The resonant frequency is f0 = 1 / (2*pi*sqrt(L*C)), known as Thomson's formula, where L is inductance in henries and C is capacitance in farads. For L = 100 mH and C = 1 microfarad, f0 = 1 / (2*pi*sqrt(0.1 * 0.000001)) = 503.29 Hz.
How do you find the inductance needed for a target resonant frequency?
Rearrange Thomson's formula to L = 1 / ((2*pi*f0)^2 * C). Given a target f0 and a known capacitance C, this gives the exact inductance required. For f0 = 503.29 Hz and C = 1 microfarad, L works out to 100.00 mH, recovering the original example.
How do you find the capacitance needed for a target resonant frequency?
Rearrange Thomson's formula to C = 1 / ((2*pi*f0)^2 * L). Given a target f0 and a known inductance L, this gives the exact capacitance required. For f0 = 503.29 Hz and L = 100 mH, C works out to 1.00 microfarad.
Does resistance affect the resonant frequency of an LC circuit?
No, ideal resonant frequency f0 = 1/(2*pi*sqrt(LC)) depends only on inductance and capacitance. In a real series RLC circuit, resistance does not shift f0, it only affects how sharp or damped the resonance peak is, which is measured by the quality factor Q.
What is angular resonant frequency?
Angular resonant frequency omega0 = 2*pi*f0, measured in radians per second, is the same resonance expressed in angular terms instead of cycles per second (hertz). It appears directly in the impedance formulas for inductors (omega*L) and capacitors (1/(omega*C)).
Why do AM radio tuning circuits use an LC resonant circuit?
An LC tank circuit resonates at a specific frequency and rejects others, letting a radio receiver select one station's signal out of many broadcasting at different frequencies. For example, L = 200 microhenries and C = 300 picofarads gives f0 = 649.75 kHz, which falls inside the AM broadcast band.
What units does this calculator use for L and C?
Inductance is entered in millihenries (mH) in the Find f0 and Find C modes, and the result of Find L mode is shown in mH or microhenries depending on size. Capacitance is entered in microfarads (uF), and Find C mode results auto-scale to nanofarads or picofarads for very small values.
How does doubling capacitance change the resonant frequency?
Because f0 is proportional to 1/sqrt(C), doubling capacitance lowers the resonant frequency by a factor of 1/sqrt(2), about a 29% reduction, not a 50% reduction. The same 1/sqrt scaling applies to changes in inductance.
Can this calculator solve for L, C, and f0 all from each other?
Yes. Use the Find f0 mode when you know L and C, the Find L mode when you know the target f0 and C, and the Find C mode when you know the target f0 and L. All three modes use the same underlying Thomson's formula, just rearranged for the unknown you need.
Why is my calculated resonant frequency different from what I measured on a real circuit?
Real components have parasitic effects, stray capacitance in wiring, equivalent series resistance in capacitors, and self-capacitance in inductors, that shift the actual resonant frequency slightly from the ideal Thomson's formula value. Component tolerance (often 5-20% for capacitors) also contributes.