Free LC Resonant Frequency Calculator | Inductor-Capacitor Circuit
Free calculator for LC resonant circuits made of an inductor (L) and capacitor (C). Solve for frequency, inductance, or capacitance from the other two values, plus characteristic impedance.
What Is an LC Resonant Circuit?
A circuit built from a coil (L) and a capacitor (C) lets current flow most easily at one particular frequency — or, depending on the configuration, blocks it most strongly at that same frequency. That frequency is called the resonant frequency, and it is found with Thomson's formula, f = 1 / (2π√(LC)). This calculator lets you enter any two of frequency, inductance, and capacitance and it works out the third, while also showing the characteristic impedance of the LC pair.
The numbers this tool returns are theoretical values that assume ideal components. Real-world coils and capacitors carry parasitic elements — winding resistance in the coil, equivalent series resistance (ESR) in the capacitor — so a measured resonant frequency will typically sit slightly off the calculated value. Because you can pick units such as H, mH, µH, and nH for inductance, or pF, nF, µF, and mF for capacitance, you can type in the exact figures printed on your components without converting them by hand first.
How to Calculate LC Resonant Frequency
- Choose which value to solve for Pick whether you want resonant frequency, inductance, or capacitance calculated. The input field for that value hides automatically once selected.
- Enter the two known values Type in the figures exactly as printed on your components — the unit dropdowns let you stay in µH or pF without converting manually.
- Read the result and characteristic impedance Along with the value you solved for, the calculator also shows the characteristic impedance Z₀, a handy reference when you are thinking about impedance matching.
Tips for getting more out of it
- Switch "Value to solve for" to derive resonant frequency, inductance, or capacitance from the other two values — handy for radio tuning circuits or filter design.
- Real circuits have parasitic elements such as coil winding resistance and a capacitor's equivalent series resistance (ESR), so the actual resonant frequency can differ slightly from the ideal formula's result.
- Characteristic impedance (Z₀) is a useful reference when designing RF filters or antenna matching networks, to check how well it matches the load impedance.
- Choose units from H/mH/µH/nH, F/mF/µF/nF/pF, and Hz/kHz/MHz/GHz so you can enter values exactly as printed on the component (e.g. 100µH, 220pF).
Where LC Resonant Frequency Calculations Are Used
Designing a receiver's tuning circuit
Work backward from a target broadcast frequency to figure out the coil and capacitor values you need, or to decide the tuning range a variable capacitor should cover.
Choosing filter component values
Starting from the boundary between the band you want to pass and the band you want to block, derive the L and C values a filter needs — useful groundwork for noise-suppression circuit design.
Checking whether parts on hand will work
Plug in the values of coils and capacitors already in your parts bin to see what frequency they resonate at, before deciding whether you need to order anything new.
Comparing theory against a measured result
Calculate the ideal resonant frequency first, then compare it with what you actually measure on the bench to estimate how much parasitic resistance is affecting the circuit.
LC Resonant Circuit Terms
- Inductance
- A measure of how strongly a coil opposes a change in current. It is measured in henries (H); practical circuits commonly use µH or mH.
- Capacitance
- A measure of how much electric charge a capacitor can store. It is measured in farads (F), though real components are usually specified in pF or µF.
- Resonant frequency
- The frequency at which the coil's and capacitor's reactances cancel each other out. The circuit's response is at its maximum or minimum at exactly this point.
- Characteristic impedance
- The value obtained from the square root of the ratio of L to C. It serves as a benchmark when matching the circuit to another circuit or load.
- Thomson's formula
- The equation used to find resonant frequency, written as f = 1 / (2π√(LC)). The frequency depends only on the product of L and C.
- ESR (equivalent series resistance)
- The small resistive component present in a real capacitor. It dampens the sharpness of resonance and is one reason measured results deviate from theory.
- Quality factor (Q)
- A number describing how sharp and low-loss a resonant circuit is. A higher Q means a narrower resonance peak and less energy lost per cycle.
- Reactance
- The frequency-dependent opposition to current offered by a coil or capacitor. At resonance, the inductive and capacitive reactances are equal in magnitude and cancel out.
Frequently Asked Questions
Side Note — LC Resonant Circuits and the History of Radio
The principle of the LC resonant circuit was established in the late 19th century and underpinned the practical development of radio broadcasting in the early 20th century. Early radio receivers had to pick out only the desired station's frequency from the faint radio waves picked up by the antenna, which they did by varying a capacitor's capacitance to shift the resonant frequency to match the target station — an operation known as "tuning."
William Thomson (later Lord Kelvin), whose name is attached to the formula, published a theory of electrical oscillation circuits in 1853, mathematically describing how an LC circuit resonates at a particular frequency. This formula is still used today not only in radio and television tuners, but across a wide range of fields including wireless transmit/receive circuits, noise-rejection filters, and metal detectors.
Modern tuning methods rely mainly on digital signal processing and PLLs (phase-locked loops), but the LC resonant circuit as an analog building block remains one of the first topics taught in electrical engineering curricula, still foundational to high-frequency circuit design today.