📻 Resonance Tool

LC Resonant Frequency Calculator — f₀ = 1/(2π√LC), Parallel & Series Tank, Q Factor & Bandwidth

Set any inductance and capacitance — the calculator returns f₀, characteristic impedance Z₀, Q factor and bandwidth live, for both series and parallel tank topologies, with a capacitor self-resonance warning built into the physics.

LC Resonant Frequency Calculator

f₀ = 1/(2π√LC) — live resonance, Z₀, Q factor and bandwidth readout.

Inductance (L)

10 nHlog scale100 mH

Capacitance (C)

1 pFlog scale100 µF

Quick presets

Tank topology

Series resistance R (Ω)

Q = Z₀ / R — series loss sets the tank's damping.

Resonant frequency f₀

1.5915MHz

Z₀ = √(L/C)

100 Ω

Q factor

BW = f₀/Q

159.15 kHz

Ideal Q vs practical Q (ESR 0.5 Ω)

Ideal Q (lossless C)10

Practical Q — Q·(1 − ESR/Z₀)9.95

When Z₀ = 100 Ω, an ESR of 0.5 Ω removes 0.5% of the tank's Q. Small Z₀ tanks suffer the most.

The derivation

How to Calculate Resonant Frequency of LC Circuit

Every LC resonance question reduces to one equality: at the resonant frequency, inductive reactance and capacitive reactance are exactly equal in magnitude. Inductive reactance rises with frequency, X_L = 2πfL; capacitive reactance falls, X_C = 1/(2πfC). When parameter f moves upward, X_L climbs linearly while X_C falls as 1/f — so the two curves always cross at exactly one frequency. Setting X_L = X_C gives 2πfL = 1/(2πfC), and solving for f produces f₀ = 1/(2π√(LC)). Square the answer away from algebra: multiply L by C, take the square root, multiply by 2π, invert. That is the entire calculation — no approximations, no fudge factors, valid from 1 Hz to 1 GHz as long as the parts are behaving.

Exact formula

f₀ = 1 / (2π√(L·C))

from X_L = 2πf·L = X_C = 1/(2πf·C)

L in henries, C in farads → f₀ in hertz. Every unit prefix must be converted before the multiply: 10 µH is 1 × 10⁻⁵ H, 1 nF is 1 × 10⁻⁹ F.

Using an Inductor Capacitor Resonant Frequency Calculator Step by Step

An inductor capacitor resonant frequency calculator is a unit-discipline exercise more than a mathematics exercise. Step one: convert L to henries and C to farads. Step two: form the product LC. Step three: take the square root. Step four: divide 1 by 2π times that root. When L = 10 µH and C = 1 nF, the product is 1 × 10⁻¹⁴, the root is 1 × 10⁻⁷, and f₀ = 1/(2π × 10⁻⁷) = 1.5915 MHz. Now watch the sensitivity: if C moves from 1 nF to 10 nF, the product grows tenfold, the root grows only 3.16×, and f₀ drops to 503 kHz. A ×10 change in either component buys only a ÷3.16 change in frequency — that square root is why tank tuning feels coarse at the top of a band and fine at the bottom.

Worked Examples You Can Verify in the Tool

Take the calculator's default pair: 10 µH against 1 nF gives f₀ = 1.5915 MHz, Z₀ = √(10 µH ÷ 1 nF) = 100 Ω — a workable impedance for a small-signal transistor stage. Move the preset buttons and the readout follows: a 100 µH coil with 10 nF lands at 159.2 kHz in the AM broadcast band, while 100 nH with 10 pF reaches 159.2 MHz in VHF. The same f₀ can always be reached by many L/C pairs; what changes between them is Z₀, and Z₀ is what decides how the tank interacts with the rest of the circuit. Verify X_L and X_C separately at f₀ with the capacitor reactance calculator — at resonance the two reactances are mirror images.

Electronics workbench with an oscilloscope and inductor-capacitor test setup used to measure LC tank resonance

f₀ is where X_L and X_C crossPhoto: Unsplash

Reference

LC Tank Resonant Frequency — Common L & C Pairs

Read this table as a design map rather than a derivation. Each row pairs a coil value you can actually buy or wind with a capacitor value that is standard catalog stock, and the bandwidth column assumes Q = 50, so BW = f₀/50. Pick the row nearest your application, then open the calculator above, plug in the pair, and adjust until the readout matches your target frequency.

Inductance (L)	Capacitance (C)	f₀ Resonant Freq	Bandwidth @ Q=50	Typical Use
10 µH	10 nF	503 kHz	10.1 kHz	Audio
100 µH	10 nF	159 kHz	3.18 kHz	AM radio
1 µH	100 pF	15.9 MHz	318 kHz	RF
100 nH	10 pF	159 MHz	3.18 MHz	VHF

This LC resonant frequency calculator is one tool in a wider capacitor toolkit — the Capacitor Calculator home page covers code decoding, unit conversion and the core capacitor formulas, and the calculators hub links every tool on the site, from reactance to RC filtering.

Topology behavior

How a Capacitor Inductor Resonance Calculator Treats Series and Parallel Tanks

The f₀ formula never changes between topologies — 1/(2π√LC) is a property of the L and C pair itself. What changes is what the tank does to the circuit around it, and that inversion is where most build mistakes happen. A capacitor inductor resonance calculator that only prints f₀ is half a tool; the useful half is the impedance behavior at f₀, because that decides whether the tank belongs in series with your signal path or in parallel with it.

⚡ Topology rule. At resonance, a parallel LC tank has maximum impedance (infinite in the ideal case), while a series LC has minimum impedance (zero ideal). This inversion is critical for selecting the right topology for your filter.

Series LC: the Notch and the Impedance Minimum

Place L and C in series with a signal path and the branch impedance is Z = R + j(ωL − 1/ωC). At f₀ the imaginary terms cancel and only the residual series resistance remains — when parameter f = f₀, the branch state moves from blocking to nearly a dead short. That is exactly what a wave trap does: put a series tank across an antenna input tuned to an interfering station and it shorts that one frequency to ground while leaving every other frequency almost untouched. The depth of the notch is set by Q = Z₀/R_series. With Z₀ = 100 Ω and R = 10 Ω, Q = 10 and the notch is 159 kHz wide at the −3 dB points for a 1.59 MHz tank — broad enough to swallow a whole broadcast channel.

Parallel LC: the Tank That Selects One Frequency

Wire the same pair in parallel and the behavior inverts. Below f₀ the inductor passes current and the branch looks inductive; above f₀ the capacitor takes over and the branch looks capacitive; at f₀ the two circulating currents cancel and the branch impedance peaks. In a regenerative or superheterodyne receiver, that peak becomes the collector load of a transistor: DC bias passes straight through the inductor, while the amplified signal at f₀ sees a high-impedance load and develops maximum voltage. Set the same 10 µH + 1 nF pair in parallel with R = 100 kΩ of load and Q = R/Z₀ = 1000, so the response narrows to 1.59 kHz — a hundred times sharper than the series version, because the large parallel resistance barely damps the tank. Swap the R input in the calculator above and watch Q and bandwidth move in opposite directions: raise R in parallel mode and the tank sharpens; raise R in series mode and the notch widens.

Sharpness

Q Factor and Bandwidth — What a Resonance Capacitor Calculator Should Tell You

Q is the quality factor: the ratio of energy stored in the tank to energy lost per cycle, multiplied by 2π. In frequency-domain terms it converts to a single clean identity, Q = f₀/BW, where BW is the separation between the −3 dB half-power points. A resonance capacitor calculator that reports f₀ alone leaves you blind here — two tanks at exactly 1 MHz can behave completely differently if one has Q = 10 and the other Q = 200. The first is 100 kHz wide and rings for roughly Q/π ≈ 3 cycles after a disturbance; the second is 5 kHz wide and rings for roughly 64 cycles. Q is also where topology matters again: a series resistance R gives Q = Z₀/R, while a parallel load R gives Q = R/Z₀. The same ohms move Q in opposite directions depending on where they sit.

The table below lists the Q targets that real applications demand. Note how brutal the spread is: an audio crossover tolerates a sloppy tank, a crystal does not.

Application	Typical Q	BW if f₀ = 1 MHz
Audio crossover / equalizer LC	3–10	100–333 kHz
AM ferrite-rod tank, 455 kHz IF	50–100	10–20 kHz
Shortwave / VHF resonant tank	100+	under 10 kHz
Quartz crystal resonator	10,000+	under 100 Hz

💡 Tip. For an AM radio coil, target Q between 50 and 100. At the 455 kHz IF, Q = 50 gives BW = 9.1 kHz — just inside the 10 kHz channel spacing, so one station's sidebands pass while the neighbours are rejected. Winding the coil with Litz wire and keeping it away from metal raises Q for free; a ferrite rod does the same job by concentrating the flux.

⚠️ Warning. Do not chase an arbitrarily high Q in a loaded tank. Every load you hang on the output appears as an equivalent resistance and divides Q downward — a Q = 1000 coil driving a 100 kΩ load through Z₀ = 100 Ω drops to an effective Q = 500. Design Q in the loaded condition, not the datasheet condition, or your bandwidth prediction will be off by the ratio of the two resistances.

Tank Capacitor Calculator: Choosing C When Q Matters

A tank capacitor calculator earns its keep at this step, because for a fixed f₀ you can trade L against C freely — and the trade moves Z₀, which moves loaded Q. High L with low C pushes Z₀ up: a 100 µH + 1 nF pair at 503 kHz has Z₀ = 316 Ω, so a modest 10 kΩ parallel load still leaves Q = 31. Low L with high C pushes Z₀ down toward the ESR floor, where the capacitor's own losses start to eat the tank — the practical-Q bar in the calculator shows exactly this collapse when Z₀ approaches the assumed 0.5 Ω ESR. When the application demands Q above 10,000, no LC pair will get you there; that is crystal territory, and the crystal oscillator capacitor calculator takes over where the tank ends.

Macro photograph of surface-mount ceramic capacitors on a printed circuit board, the parts whose parasitic inductance sets the self-resonant frequency

Above SRF, your capacitor is an inductorPhoto: Unsplash

Physical limit

Capacitor Self-Resonance (SRF): the Parasitic Limit

Parasitic Limit

⚠️ Warning. Every real capacitor has a Self-Resonant Frequency (SRF) — above this point the capacitor looks inductive. The SRF is set by the capacitor's parasitic lead inductance; for surface-mount caps it's typically 50–500 MHz.

What a Capacitor SRF Calculator Warns About

A capacitor is never just C — it is C in series with a parasitic inductance (ESL) and an ESR, the whole network forming a hidden series RLC. Below SRF the capacitance dominates and the part behaves as expected; at SRF the impedance bottoms out at the ESR; above SRF the ESL dominates and impedance climbs with frequency, exactly like an inductor. That is why a 1 µF electrolytic can be useless as a decoupling capacitor at 100 MHz while a 10 nF 0402 ceramic is excellent there — the electrolytic's SRF has been left far behind, the 0402's has not.

Capacitor Style	Parasitic L (typical)	SRF Window
Through-hole electrolytic	10–100 nH	0.1–1 MHz
Radial film box capacitor	5–20 nH	1–10 MHz
0805 MLCC (ceramic)	0.5–1 nH	10–100 MHz
0402 MLCC (ceramic)	0.2–0.5 nH	50–500 MHz

Checking SRF with a Capacitor Self Resonance Calculator

The SRF formula is the tank formula applied to the parasite: SRF = 1/(2π√(L_parasitic·C)). Run one number through it by hand: a 100 nF capacitor carrying 1 nH of effective series inductance gives √(10⁻⁷ × 10⁻⁹) = √10⁻¹⁶ = 10⁻⁸, so SRF = 1/(2π × 10⁻⁸) ≈ 15.9 MHz. Above 15.9 MHz that 100 nF part contributes inductance, not capacitance. The design rule that falls out of every capacitor self resonance calculator is simple: pick a capacitor whose SRF is at least 10× your circuit frequency, and shrink the package (0805 → 0402) when you need to push the ceiling higher. For tank duty at RF this is not optional — a tank capacitor operating above its own SRF adds inductance to the tank, and the actual resonant frequency lands below the value printed by any formula.

The same parasitic logic explains why the capacitor page family matters: reactance, SRF and ESR are three views of the same real-world part, and a tank design is only as honest as the weakest of the three models.

Tolerances

Why Real LC Tanks Drift — Tolerance, Temperature and Strays

The formula is exact; the components are not. Inductors are the loosest parts in the signal chain: a standard off-the-shelf choke carries ±10% tolerance, and a hand-wound coil can be ±20% before you ever measure it. Capacitors split by dielectric — C0G/NP0 ceramics hold ±5% or better with a ±30 ppm/°C drift, while X7R parts carry ±15% over the −55 °C to +125 °C range and additionally lose capacitance under DC bias. Compound the headline tolerances and the arithmetic is sobering: when L runs +10% and C runs +5%, f₀ = 1/(2π√(1.10 × 1.05 × LC)) falls about 7.3% below nominal. On a 1.59 MHz tank that is a 116 kHz error — larger than a whole AM channel.

Strays pile on top. A solderless breadboard contributes 2–20 pF per node, and every centimetre of component lead adds roughly 10 nH of series inductance. With a 100 pF tank capacitor, 10 pF of stray is a 10% capacitance error, worth about −5% in frequency. The professional answer is not better arithmetic — it is a trimmer: put a small 2–30 pF variable capacitor in place of, or in parallel with, the fixed C, align the tank on the bench at the operating temperature, and let the calibration absorb every tolerance at once.

The Coil Capacitor Frequency Calculator Workflow Starts with a Measured L

A disciplined coil capacitor frequency calculator workflow inverts the usual order: measure the coil first, then compute the capacitor. Wind or select the inductor, measure its actual value with an LCR meter at a frequency near your operating point (inductance readings drift with test frequency for ferrite-cored parts), then feed the measured L into the calculator and solve C = 1/((2πf₀)²L). If you need a first-order roll-off rather than a resonant peak — a tone control or a supply filter rather than a tank — the same measured components slot into the RC filter capacitor calculator instead, where fc = 1/(2πRC) replaces the √LC expression.

⚠️ Warning. Class-2 ceramics (X7R, X5R) lose capacitance under DC bias — a 10 nF X7R rated 50 V sitting across a 25 V bias can deliver 20–30% less than its marked value, and the loss reverses as temperature moves. A tank built on X7R drifts every time the radio warms up. For any resonant duty, specify C0G/NP0 or film; the capacitance costs more volume, but f₀ stays where you aligned it.

❌ Don't. Don't use an electrolytic or a big through-hole film capacitor as an RF tank capacitor — its 10–100 nH of lead inductance puts the SRF near or below your circuit frequency, and above SRF the part is an inductor wearing a capacitor's label. Don't trust breadboard strays either: a tank below about 500 kHz can live with 10 pF of stray, but a 15 MHz VHF tank cannot, because 10 pF is 100% error against a 10 pF design capacitor. Move the finished tank to soldered construction and realign.

Questions About LC Resonance, Q and Bandwidth

How do I calculate the resonant frequency of an LC circuit?▼

Set the reactances equal: 2πfL = 1/(2πfC). Solve for f and you get f₀ = 1/(2π√(LC)), with L in henries and C in farads. For a 10 µH coil and a 1 nF capacitor, LC = 1 × 10⁻¹⁴ and f₀ = 1/(2π × 10⁻⁷) ≈ 1.592 MHz. The calculator at the top of this page runs the same arithmetic live and adds Z₀, Q factor and bandwidth on top.

What is a tank capacitor calculator used for?▼

It sizes the capacitor you pair with a coil to hit a target frequency. Rearranged, C = 1/((2πf₀)²L): a 159 kHz tank built on a 100 µH coil needs C = 10 nF. A tank capacitor calculator also surfaces the secondary numbers — Z₀ = √(L/C), Q and bandwidth — that decide whether the finished tank will drive the load you have in mind.

What is capacitor self-resonance (SRF)?▼

Every real capacitor carries a fraction of a nanohenry of parasitic lead inductance in series with its capacitance. That hidden LC pair resonates at the self-resonant frequency; above it the part's impedance rises with frequency, meaning it behaves inductively. A 100 nF part with 1 nH of ESL self-resonates near 15.9 MHz. For tank duty, pick a capacitor whose SRF is at least 10× your circuit frequency.

Series or parallel LC tank — which do I need?▼

Series LC has minimum impedance at f₀ — use it to short one specific frequency to ground, i.e. a notch filter or wave trap. Parallel LC has maximum impedance at f₀ — use it as a high-Q load that blocks f₀ while passing DC, the classic transistor collector tank or oscillator frequency selector. If you must remove one frequency, go series; if you must select one frequency, go parallel.

How does Q relate to bandwidth?▼

Bandwidth BW = f₀/Q exactly, measured between the −3 dB half-power points. A 1 MHz tank with Q = 50 is 20 kHz wide; the same tank at Q = 200 narrows to 5 kHz. Doubling Q halves the bandwidth and doubles the number of ring-down cycles. Q is set by whichever resistance dominates: series R gives Q = Z₀/R, parallel R gives Q = R/Z₀.

What Q should my AM radio coil have?▼

Aim for 50–100. The AM channel spacing is 10 kHz and the standard IF is 455 kHz: a ferrite-rod coil with Q = 50 gives BW = 9.1 kHz, wide enough to pass one station's sidebands while rejecting the neighbours. Push Q much above 100 and the high audio frequencies get clipped; let it fall below 40 and adjacent-channel stations bleed through.

Why does my LC circuit resonate at the wrong frequency?▼

Usually strays. A breadboard adds 2–20 pF of stray capacitance per node, and every centimetre of lead adds roughly 10 nH; with a 100 pF tank capacitor, just 10 pF of stray shifts f₀ down by about 5%. Tolerance compounds it: a ±10% inductor with a ±5% capacitor can land anywhere from −7% to +8% of nominal. Measure the assembled circuit, then trim — a small trimmer capacitor in place of fixed C is the standard fix.

Does ESR change the resonant frequency?▼

Barely — which is why the practical-Q bar in the calculator matters more than a frequency correction. In a series RLC branch the frequency where X_L = X_C is independent of R; ESR only flattens the impedance dip and lowers Q. In a parallel tank the damped resonance shifts to f_d = f₀·√(1 − 1/(4Q²)): at Q = 10 that is only −0.13%. ESR's real cost is Q and bandwidth, not frequency.

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