Electronics calculator

Free Resonant Frequency (LC) calculator

Enter your inductor and capacitor values and this calculator returns the LC resonant frequency f = 1/(2π√(LC)) — in hertz, kilohertz and megahertz — or reverse it to size the L or C you need for a target frequency, updated live, as you type.

InputsLive
What do you want to solve for?
Inductance unit
Inductance (L)
µH
Capacitance unit
Capacitance (C)
pF
Result
Resonant frequency
1.5915 MHz
The frequency this L–C pair oscillates at most readily.
In hertz1,591,549 Hz
In kilohertz1,591.55 kHz
Angular ω10,000,000 rad/s

Ideal-circuit estimates from the values you enter. Verify against your real components.

Results are estimates. Consult a professional.

How it's calculated

How the resonant frequency calculator works

An inductor and a capacitor wired together form a resonant circuit, also called a tank circuit. At one special frequency the energy sloshes back and forth between the two parts with the least opposition. This calculator finds that frequency from the inductance and capacitance you enter. It converts your practical units — microhenries, millihenries, picofarads, nanofarads — to base units, runs the formula, and reports the answer in hertz, kilohertz and megahertz at once.

f = 1 / (2π × √(L × C))
ω =× f = 1 / √(L × C)
The relation f = 1/(2π√(LC)) is standard LC-circuit theory: at resonance the inductive reactance equals the capacitive reactance, so they cancel. See Wikipedia's "LC circuit" article and The ARRL Handbook for Radio Communications.
The formula

The LC resonant frequency formula explained

Three quantities drive the result, and each one pulls the frequency in a predictable direction. Read the formula once and you can estimate any LC circuit in your head.

Inductance (L) — the magnetic store

Inductance measures how strongly a coil opposes a change in current by storing energy in a magnetic field. Larger inductance lowers the resonant frequency. Because L sits under a square root, multiplying it by four only halves the frequency, not quarters it.

Capacitance (C) — the electric store

Capacitance measures how much charge a capacitor holds for a given voltage, storing energy in an electric field. Larger capacitance also lowers the frequency, and it sits under the same square root, so it behaves exactly like inductance in the math.

The square root and the 2π

The product L × C sets the timing of the oscillation; its square root gives the period, and the 2π converts the raw angular rate into ordinary cycles per second. The headline rule: to push the frequency up, make either component smaller; to bring it down, make either component bigger.

Square-root scaling
Because both L and C are under the square root, a 100× change in either one shifts the frequency by only 10×. That is why tuning circuits use a small variable component for fine control rather than swapping large parts.
Example

A worked example using the resonant frequency calculator

Example: a 100 µH coil with a 100 pF capacitor

Priya is designing a small radio-frequency tank circuit. She has a 100 µH inductor and a 100 pF capacitor on the bench and wants to know the frequency the pair will resonate at before she breadboards it.

Step 1 — Convert to base units

100 µH = 0.0001 H and 100 pF = 0.0000000001 F (that is 1×10⁻⁴ H and 1×10⁻¹⁰ F).

Step 2 — Multiply L by C

L × C = 1×10⁻⁴ × 1×10⁻¹⁰ = 1×10⁻¹⁴. Its square root is 1×10⁻⁷.

Step 3 — Apply the formula

f = 1 ÷ (2π × 1×10⁻⁷) = 1,591,549 Hz, which is 1591.55 kHz or about 1.5915 MHz. The angular frequency ω is a clean 1×10⁷ rad/s.

1.5915 MHz (1591.55 kHz)
That sits in the AM broadcast band, so this LC pair could tune a simple medium-wave receiver. To shift it lower, Priya would add capacitance or inductance; to shift it higher, she would reduce either one.
Reverse the math

Solving for L or C at a target frequency

Most real design work runs the formula backwards. You know the frequency you want and one component you already have, and you need the value of the missing part. Rearranging f = 1/(2π√(LC)) gives two direct expressions.

L = 1 / ((2πf)² × C)
C = 1 / ((2πf)² × L)

Worked the other way: to tune a 100 µH coil to the 455 kHz intermediate frequency used in superheterodyne radios, the capacitor needs to be C = 1 ÷ ((2π × 455,000)² × 0.0001) = 1223.54 pF. You would reach that with a fixed 1000 pF capacitor plus a small trimmer.

Why a trimmer capacitor
Calculated values rarely match stock parts exactly. Designers pick the nearest standard component, then add a small variable capacitor or inductor to fine-tune the circuit onto the exact target frequency.
Quick reference

Resonant frequency quick-reference table

These common inductor-capacitor pairs give a feel for how the frequency moves. Every value here comes straight from the formula above.

InductanceCapacitanceResonant frequency
1 mH1 µF5.03 kHz
1 mH220 pF339.32 kHz
100 µH1 nF503.29 kHz
100 µH100 pF1.59 MHz
10 µH100 pF5.03 MHz
2.2 µH220 pF7.23 MHz
1 µH10 pF50.33 MHz

Computed from f = 1/(2π√(LC)). Halving both L and C raises the frequency by 2×; the square-root scaling means each tenfold drop in the L×C product roughly triples the frequency.

Applications

Where LC resonance is used

Resonant LC circuits are everywhere a circuit needs to favour one frequency over all the others. The resonant frequency is the dividing line that decides what passes and what gets blocked.

  • Radio tuning — turning the dial changes a variable capacitor, sliding the resonant frequency onto the station you want.
  • Band-pass and band-stop filters — an LC section passes a band of frequencies around resonance, or notches one out, in audio and RF signal paths.
  • Oscillators — an LC tank sets the frequency of LC oscillators such as the Colpitts and Hartley designs that generate clean sine waves.
  • Impedance matching and traps — antenna systems use LC resonance to match impedances and to trap unwanted frequencies.
  • Wireless power and RFID — transmitter and receiver coils are tuned to the same resonant frequency so energy couples efficiently.

The companion voltage divider calculator handles the resistive side of analog design, while Ohm's law covers the current and power once you know the circuit values.

Circuit type

Series vs parallel LC circuits

A frequent point of confusion is whether the components sit in series or in parallel. The resonant frequency formula is identical for both — f = 1/(2π√(LC)) — but the behaviour at that frequency is opposite.

PropertySeries LCParallel LC (tank)
Impedance at resonanceMinimum (near zero)Maximum (near infinite)
Current at resonanceMaximumMinimum from the source
Acts asBand-pass / acceptorBand-stop / rejector
Resonant frequency1/(2π√(LC))1/(2π√(LC))

For an ideal lossless circuit the resonant frequency is the same; resistance in real parts shifts the parallel-circuit peak very slightly.

In short, a series LC lets the resonant frequency through, and a parallel LC blocks it. Designers choose the arrangement by whether they want to select a frequency or reject one.

Definitions

Resonant-circuit definitions

The frequency at which an LC circuit oscillates most readily, where inductive and capacitive reactance are equal and cancel. Given by f = 1/(2π√(LC)).
A coil's opposition to a change in current, measured in henries (H). Practical values run from microhenries (µH) in RF coils to henries in power chokes.
A capacitor's ability to store charge per volt, measured in farads (F). Tuning capacitors are typically picofarads (pF) to nanofarads (nF).
The frequency-dependent opposition of an inductor or capacitor to alternating current. At resonance the inductive and capacitive reactances are equal.
Frequency expressed in radians per second rather than cycles per second: ω = 2πf = 1/√(LC). Common in circuit equations because it removes the 2π.
A parallel LC circuit that stores energy oscillating between the coil and the capacitor, named for the way it holds a reservoir of energy at its resonant frequency.
A measure of how sharp the resonance is — how narrowly the circuit selects its resonant frequency. Higher Q means a narrower, more selective peak.
Accuracy

How accurate is this resonant frequency calculator

The math is exact. For the inductance and capacitance you enter, f = 1/(2π√(LC)) is the precise resonant frequency of an ideal lossless circuit, computed to full floating-point precision and then converted between hertz, kilohertz and megahertz.

Real circuits drift from the ideal for physical reasons, not arithmetic ones. Capacitors and inductors carry tolerances of 5 to 20 percent, so the built circuit lands near the calculated frequency rather than exactly on it. Stray capacitance from the wiring, the resistance of real coils, and temperature all nudge the result. Treat the calculated value as the design target, then trim the circuit with a variable component to hit the exact frequency. For the underlying theory, the Wikipedia "LC circuit" article and standard electronics references give the full derivation.

Questions

Frequently asked questions about the free Resonant Frequency (LC) calculator

A resonant Frequency (LC) calculator is a free online tool that helps you find the resonant frequency of an LC circuit from inductance and capacitance — or solve for the L or C needed to hit a target frequency. An inductor and capacitor resonate where their reactances cancel. The resonant frequency depends only on the product of L and C. It runs entirely in your browser with instant results and no sign-up.
Using f = 1/(2π√(LC)) with L = 0.001 H and C = 2.2×10⁻¹⁰ F gives about 339.32 kHz. That is the frequency this LC pair oscillates at most readily.
Yes — both use f = 1/(2π√(LC)). The behaviour differs: a series LC has minimum impedance at resonance (it passes that frequency), while a parallel LC has maximum impedance (it blocks it).
Rearrange the formula: C = 1/((2πf)²L) or L = 1/((2πf)²C). Switch the calculator's mode to solve for L or C, enter the target frequency and the part you have, and it returns the value needed.
A radio's tuning circuit is an LC tank. Turning the dial changes a variable capacitor, which slides the resonant frequency onto the station's broadcast frequency so that signal is amplified above the rest.
Components carry 5–20% tolerance, and stray capacitance, coil resistance and temperature all shift the result. Treat the calculated value as the design target and trim with a small variable capacitor or inductor.
About

About this Resonant Frequency (LC) calculator

This calculator runs entirely in your browser — nothing you enter is sent anywhere. It applies the standard LC resonance formula f = 1/(2π√(LC)), converts your µH/mH/H and pF/nF/µF inputs to base units, and can solve in any direction: frequency from L and C, or the L or C needed for a target frequency.

Built for hobbyists, students and RF designers sizing tank circuits, filters and oscillators. Browse more tools in electronics calculators or see the full calculator library.

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