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.
On this page14 sections
Ideal-circuit estimates from the values you enter. Verify against your real components.
Results are estimates. Consult a professional.
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.
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.
A worked example using the resonant frequency calculator
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.
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.
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.
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.
| Inductance | Capacitance | Resonant frequency |
|---|---|---|
| 1 mH | 1 µF | 5.03 kHz |
| 1 mH | 220 pF | 339.32 kHz |
| 100 µH | 1 nF | 503.29 kHz |
| 100 µH | 100 pF | 1.59 MHz |
| 10 µH | 100 pF | 5.03 MHz |
| 2.2 µH | 220 pF | 7.23 MHz |
| 1 µH | 10 pF | 50.33 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.
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.
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.
| Property | Series LC | Parallel LC (tank) |
|---|---|---|
| Impedance at resonance | Minimum (near zero) | Maximum (near infinite) |
| Current at resonance | Maximum | Minimum from the source |
| Acts as | Band-pass / acceptor | Band-stop / rejector |
| Resonant frequency | 1/(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.
Resonant-circuit definitions
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.
Frequently asked questions about the free Resonant Frequency (LC) calculator
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.