This resonance frequency calculator finds where an LC circuit wants to oscillate — f₀ = 1/(2π√(LC)) — and reports the period, angular frequency, and the characteristic impedance where the inductor’s and capacitor’s reactances cancel exactly. Resonance is the principle behind radio tuning, wireless power, metal detectors and quartz clocks’ electronic ancestors: two energy storages trading a charge back and forth at one natural rhythm.

Resonant frequency f₀ –
Period T / angular frequency ω –
Reactance at resonance XL = XC –
Characteristic impedance √(L/C) –

At f₀ the inductive and capacitive reactances are equal and opposite: a series LC looks purely resistive (minimum impedance); a parallel LC looks like an open circuit (maximum impedance). Real circuits add loss — the quality factor Q = √(L/C)/R (series) measures how sharp the resonance is.

The LC Seesaw

A capacitor stores energy in an electric field; an inductor stores it in a magnetic field. Wire the two together and the energy sloshes: the charged capacitor discharges through the inductor, the inductor’s field collapses and recharges the capacitor with opposite polarity, and the cycle repeats at a rhythm set only by the two storage sizes — f₀ = 1/(2π√(LC)). Double either L or C and the frequency falls by √2 (×0.707); quadruple one and it halves. This is the same square-root physics as a pendulum (length ↔ LC product) and a mass on a spring, which is why “resonance” thinking transfers across all of physics.

The reactance cancellation is the measurable fingerprint: below f₀ the capacitor’s reactance (1/2πfC, falling with frequency) exceeds the inductor’s (2πfL, rising); at f₀ they meet (the results table prints the value, e.g. 100 Ω for our defaults) and the pair contributes zero net reactance. The ratio √(L/C) — characteristic impedance — quietly governs how much current circulates in the tank for a given voltage, hence how violent the resonance is. Our Inductor Calculator covers the single-component world behind XL; this page is where the two components meet.

Worked Examples (Verified)

  • 10 mH × 1 µF (defaults): √(LC) = √(10⁻⁸) = 10⁻⁴ → f₀ = 1/(2π×10⁻⁴) = 1,591.5 Hz, period 0.628 ms, XL = XC = 100.0 Ω at resonance, √(L/C) = 100 Ω. The round numbers are a designed coincidence of the defaults — real parts won’t be this tidy, and the calculator doesn’t need them to be.
  • AM radio tuning: a 240 µH coil with a variable capacitor of roughly 40–400 pF sweeps f₀ across about 0.51–1.62 MHz — essentially the entire AM broadcast band from one capacitor’s rotation. Radio tuning is this formula with a knob attached.
  • Inverse design: want 100 kHz with a fixed 100 µH inductor? Solve mode gives C = 1/((2π×10⁵)²×10⁻⁴) ≈ 25.3 nF — the standard-value 22 nF part lands at 107 kHz, which is the sort of sentence filter designers say daily.

Series vs Parallel, and the Q That Sharpens Everything

The same L and C resonate at the same f₀ in both topologies, with opposite behavior: series resonance is an impedance minimum (current peaks — used in band-pass filters and induction heating), parallel resonance an impedance maximum (the “tank” that sustains oscillator amplitude and rejects interference in radio front-ends). Loss decides how dramatic either is, captured by Q: high Q (low resistance) means a needle-sharp peak, enormous circulating currents (series) or voltages (parallel), and ringing that persists for hundreds of cycles; low Q means a broad, tame hump. Q = f₀/bandwidth ties it to measurement: sweep the frequency, find the −3 dB points, and their spacing tells you the Q of the physical build — stray resistance, core losses and capacitor ESR all included, which no ideal formula can predict and every real design must measure.

Resonance at Work

  • Wireless power (Qi, EV charging): transmitter and receiver coils are both tuned to the same f₀; the shared resonance is what carries useful power across an air gap that ordinary induction couldn’t bridge.
  • RFID and NFC: the tag’s coil + capacitor resonates at the reader’s carrier (13.56 MHz), harvesting its operating power from resonance itself.
  • Metal detectors: a search coil’s oscillator shifts frequency when eddy currents in buried metal alter its effective inductance — a resonance frequency change as a metal alarm.
  • Quartz clocks: a quartz crystal is a mechanical resonator masquerading as an LC with astronomical Q (~10⁵–10⁶) — the same formula’s behavior, perfected until clocks tick true for years on a coin cell.
  • The cautionary tales: unwanted resonance amplifies too — power-system harmonics finding a capacitor bank’s f₀, and mechanical-electrical analogies like bridge oscillations, are resonance with the sign flipped from tool to hazard.

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Frequently Asked Questions

How do you calculate resonance frequency?

f₀ = 1/(2π√(LC)), with L in henries and C in farads. For 10 mH and 1 µF: √(10⁻² × 10⁻⁶) = 10⁻⁴, so f₀ = 1/(2π×10⁻⁴) ≈ 1,591.5 Hz. This calculator also runs the equation backward — give it a target frequency and either component and it solves for the other — and reports period, angular frequency, the reactance at resonance and characteristic impedance.

What happens at resonance in an LC circuit?

The inductor’s and capacitor’s reactances cancel exactly (XL = XC), leaving only the circuit’s resistance. In series that means maximum current for a given drive voltage; in parallel, maximum impedance and large voltages circulating between L and C with little supply current. Energy oscillates between the magnetic and electric fields at f₀, decaying only through the resistive losses (the Q factor measures how slowly).

What is Q factor?

A dimensionless sharpness measure: Q = 2π × (energy stored)/(energy lost per cycle), computable for a series circuit as √(L/C)/R. High Q (50–200 in good RF coils) means a narrow, tall resonance — excellent frequency selectivity, large internal voltages/currents, and slow decay (ringing for ~Q cycles). Low Q (under ~10) means a broad, well-damped response. Bandwidth = f₀/Q connects Q to the frequency sweep you’ll actually measure.

Why does my real circuit resonate at a different frequency?

Parasitics: the inductor has winding capacitance (self-resonance), the capacitor has lead inductance, the layout adds stray capacitance to ground, and ferrite cores shift inductance with frequency, temperature and signal level. Electrolytic and Class-2 ceramic capacitors can lose 20–80% of nominal capacitance under DC bias. The formula is exact for the values the parts actually present at f₀ — which is why RF designers treat nominal values as a starting bid and trim with a variable element or a network analyzer.

Series or parallel resonance — which do I want?

Series for passing one frequency with minimum loss (band-pass filters, matching into low impedances, induction-heating work coils) and wherever you want current magnification. Parallel for selecting one frequency while rejecting others at high impedance (oscillator tanks, receiver front-ends, notch behavior when placed in series with a signal path). Same f₀ formula, opposite electrical personality — this calculator’s numbers serve both; the topology choice is about what the surrounding circuit needs to see.

How do I hit an exact frequency with standard parts?

Use the solve modes here to get the ideal value, pick the nearest standard value, then account for the difference with a small trimmer capacitor in parallel (for fine-downward tuning of f₀ via C) or by slightly gapping/adjusting the inductor. Since f₀ depends on √(LC), a 2% frequency error needs a 4% component correction — and remember both parts contribute tolerance, so worst-case error stacks their squares. Designing in a trim range of ±5% is standard practice.

Can resonance be dangerous in power systems?

Yes — parallel resonance between transformer inductance and power-factor-correction capacitance can amplify harmonic currents enormously at f₀, overheating capacitors and neutrals; utilities detune capacitor banks with series reactors to move the resonance away from the 5th and 7th harmonics for exactly this reason. The magnification that makes a radio selective makes a power network fragile: Q works for whoever owns it.

Is this resonance frequency calculator free?

Yes — free, instant, no sign-up. Solves f₀ from L and C, or either component from a target frequency, with period, reactance and characteristic impedance included.