This LC resonance calculator finds the resonant frequency of an inductor-capacitor pair — the frequency radio tuners, filters and wireless chargers are built around — or solves backward for the L or C a target frequency requires.
f = 1 ÷ (2π√(LC)) — Thomson’s Formula
An LC circuit is an energy seesaw: the capacitor’s electric field collapses into the inductor’s magnetic field and back, at a frequency set only by L and C. At that frequency the two reactances (X_L = 2πfL, X_C = 1/(2πfC)) are equal and opposite — series circuits pass maximum current, parallel circuits present maximum impedance, and a radio dial selects one station out of the spectrum. Design the parts with our Inductance Calculator and Capacitance Calculator. Part of our Physics Calculators collection.
Worked Example (Verified)
- L = 10 mH, C = 100 nF (defaults): √(LC) = √(10⁻⁹) = 3.16×10⁻⁵ → f = 5.03 kHz, period ≈ 199 µs, reactances at resonance ≈ 316 Ω each
- FM radio territory: 100 MHz needs LC = 2.53×10⁻¹⁸ — e.g. L = 100 nH with C = 25 pF; values shrink fast because f depends on the square root — a 100× frequency rise demands a 10,000× smaller LC product
- AM radio: 1 MHz with a typical 240 µH ferrite loopstick needs ≈ 105 pF — the variable capacitor’s whole job in a vintage set
- Wireless power (Qi, ~110–205 kHz) and RFID (13.56 MHz) are this formula with standards documents attached
Sharpness: The Q Factor
- Real circuits lose energy in resistance; Q = X_L/R at resonance measures peak sharpness and voltage/current magnification.
- High Q: selective filters, oscillators — and dangerous voltage multiplication in power circuits not designed for it.
- Loading matters: connecting a circuit to its load adds resistance and drags both Q and (slightly) frequency — bench measurements in-circuit are the truth.
Related Tools
- Inductance Calculator — design the coil
- Capacitance Calculator — design the capacitor
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate resonant frequency?
f = 1 ÷ (2π√(L × C)), L in henries, C in farads. 10 mH with 100 nF resonates at 5.03 kHz. Halving either component raises f by √2 (≈ 41%) — the square root rules every intuition about tuning ranges.
How do I find the capacitor for a target frequency?
Rearrange: C = 1 ÷ ((2πf)² × L). Enter your target in the optional field and the calculator solves it with your inductor. The mirror formula gives L for a chosen C — variable capacitors and variable inductors are just mechanical versions of these two equations.
Series vs parallel resonance — same frequency?
Same ideal frequency, opposite behavior: series LC at resonance is a near-short (minimum impedance, maximum current); parallel LC is a near-open (maximum impedance — the “tank” circuit of transmitters). Loss resistance shifts both slightly in practice.
What is Q factor?
Q = resonant reactance ÷ series resistance (or f₀ ÷ bandwidth). It measures selectivity and energy magnification: a Q of 100 means the circuit rings for ~100/(2π)… practically, voltage across L or C can reach Q times the supply in a series circuit at resonance — why resonant power systems command respect.
Why does my built circuit resonate at a different frequency?
Component tolerances (capacitors commonly ±10–20%), stray capacitance from layout and probes, the inductor’s self-capacitance, and core µ drifting with level and temperature. Design with margin, measure in-circuit, trim once — the formula gives the target, reality negotiates.
Is this resonance calculator free?
Yes — free, instant, no sign-up.