An inductor and a capacitor connected together form a resonant circuit — a tank, in the older engineering vocabulary — that exchanges energy back and forth at one particular frequency. At that frequency the inductive reactance and the capacitive reactance are equal in magnitude and opposite in phase, so they cancel, and the circuit behaves in a way that either passes or blocks signals sharply depending on how it is wired. This LC resonant frequency calculator finds that frequency from L and C, and works backwards to find the inductor or capacitor you need to land on a frequency you have chosen.
Arb Digital builds free calculators that give designers the numbers they will actually need next, not just the headline answer. Knowing a circuit resonates at 1.59 MHz is a start; knowing its characteristic impedance is 1 kΩ, its loaded Q is 200 and its bandwidth is about 8 kHz tells you whether the design will do its job. This page computes a frequency from component values — if you only need to move a value between microhenries and millihenries, the inductance converter does that and nothing more.
What This LC Resonant Frequency Calculator Does
Choose which of the three quantities to solve for, fill in the other two, and read the result. Every input has a unit selector spanning the range these components are actually sold in — henries down to nanohenries, farads down to picofarads, hertz up to gigahertz — because component values in this field span twelve orders of magnitude and manual prefix conversion is a reliable source of errors.
Four supporting figures come with the answer. Angular frequency ω is the form used in all the underlying reactance equations, so having it saves a conversion. Characteristic impedance, √(L/C), is the reactance of either component at resonance and sets the voltage and current levels in the tank. Q factor measures how sharply the circuit selects its resonant frequency, computed here as √(L/C) ÷ R for the series case. Bandwidth is f ÷ Q, the width between the half-power points, which is the number that determines whether a filter passes the signal you want without dragging in the one next to it.
The series resistance field defaults to a realistic small value rather than zero, because a lossless resonator does not exist. Almost all of the loss in a practical LC circuit comes from the inductor's winding resistance and core losses, which is why inductor Q usually dominates the performance of the whole tank.
How to Use It
- Pick what you are solving for. Frequency from known components is the analysis case; inductance or capacitance from a target frequency is the design case.
- Enter values with the prefix selectors. Type 100 and choose µH rather than typing 0.0001 H. It is faster and it eliminates an entire class of decimal-point mistakes.
- Enter a realistic series resistance. If you do not know it, the inductor's DC resistance is a reasonable lower bound; the true figure at frequency is higher because of skin effect and core loss.
- Check the characteristic impedance. A very high or very low value often signals an impractical component pairing even when the frequency is exactly right.
- Round to real component values, then recalculate. Capacitors and inductors come in preferred value series, so design in the ideal value, pick the nearest stock part, and run the numbers again to see where you actually land.
The Formula: How Resonant Frequency Is Calculated
Resonance occurs where inductive reactance equals capacitive reactance: XL = 2πfL and XC = 1 ÷ (2πfC). Setting them equal and solving for f gives the standard result f = 1 ÷ (2π√(LC)), with L in henries, C in farads and f in hertz. Rearranged for design, L = 1 ÷ (4π²f²C) and C = 1 ÷ (4π²f²L).
Because only the product LC appears, an infinite number of L and C pairs give the same frequency. What distinguishes them is the characteristic impedance Z₀ = √(L/C), which is the reactance of each component at resonance. A high-L, low-C tank has high impedance and develops large voltages; a low-L, high-C tank has low impedance and circulates large currents. Choosing between them is a real design decision that the frequency equation alone cannot make for you.
Work an example. Take L = 100 µH and C = 100 pF. In SI those are 1 × 10⁻⁴ H and 1 × 10⁻¹⁰ F, so LC = 1 × 10⁻¹⁴ and √(LC) = 1 × 10⁻⁷. Multiply by 2π to get 6.2832 × 10⁻⁷, and the reciprocal is 1,591,549 Hz — about 1.5915 MHz, in the middle of the AM broadcast band. Characteristic impedance is √(10⁻⁴ ÷ 10⁻¹⁰) = √(10⁶) = 1,000 Ω. With 5 Ω of series loss, Q = 1,000 ÷ 5 = 200, and the bandwidth is 1,591,549 ÷ 200 ≈ 7.96 kHz. Those are the default figures shown above, and every step is reproducible on paper.
The HyperPhysics resonant RLC circuits pages at Georgia State University derive the same relationships and explain why series and parallel resonance produce opposite impedance behaviour at the resonant point. The units involved — the henry, the farad, the ohm and the hertz — are all SI derived units, defined in the BIPM SI Brochure.
Series and Parallel Resonance Are Not the Same Circuit
The frequency formula is identical for both configurations, which is exactly why the difference is so easy to miss. What changes is what the circuit does at that frequency, and the two behaviours are opposites.
In a series LC circuit the two reactances cancel and the only thing left opposing current is the loss resistance. Impedance is at a minimum, current is at a maximum, and the circuit acts as a short circuit at resonance — useful as a notch filter to shunt one frequency to ground, or as an acceptor circuit that passes it preferentially.
In a parallel LC circuit the inductor and capacitor exchange energy between themselves, and the current circulating within the loop can be far larger than the current drawn from the source. Impedance is at a maximum, and the circuit acts as an open circuit at resonance — which is why it is the standard tuned load in oscillators and radio front ends. The circulating current in a parallel tank is roughly Q times the supply current, so a Q of 200 means a component current 200 times higher than what the source delivers. Components must be rated for that circulating current, not for the input current.
Q Factor and Why Bandwidth Follows From It
Q is the ratio of energy stored to energy lost per cycle, and it determines how sharply the circuit discriminates between frequencies. For a series circuit Q = √(L/C) ÷ R, which is the form used here. High Q means a narrow, sharp response; low Q means a broad, gentle one.
Bandwidth follows directly as BW = f ÷ Q, measured between the two frequencies where the response has fallen to half its peak power — the −3 dB points. This is the single most practical output of the whole calculation. A tuned circuit intended to receive an AM broadcast station needs roughly 10 kHz of bandwidth to pass the audio sidebands; too narrow and the sound loses its treble, too wide and the adjacent station comes through with it.
Raising Q means lowering loss, which in practice means a better inductor: thicker wire, litz wire at medium frequencies, an air core or a low-loss ferrite instead of a lossy one. It also means choosing a higher characteristic impedance for a given frequency, since Q rises with √(L/C) for a fixed R. That is a genuine trade-off, because very high-impedance tanks are more susceptible to stray capacitance and to loading by whatever is connected to them.
Why Your Built Circuit Lands Off the Calculated Frequency
Almost every practical LC circuit resonates slightly below its calculated frequency, and there are three usual reasons. Stray capacitance is the largest: circuit board traces, the inductor's own inter-winding capacitance and the input capacitance of whatever follows all add to C. A few picofarads is nothing against a 1 µF capacitor and is a significant fraction of a 20 pF one, which is why the effect is most visible at high frequencies where capacitors are small.
Component tolerance is the second. Ordinary capacitors are commonly ±10 or ±20 percent, and inductors are frequently worse. Since frequency depends on the square root of the product, a 10 percent error in each component shifts the frequency by about 10 percent — noticeable but not catastrophic, which is one small mercy of the square-root relationship.
The third is that component values are not constant. Ceramic capacitors of Class 2 dielectrics lose capacitance with applied DC bias, sometimes dramatically, and both L and C drift with temperature. Ferrite-cored inductors change with both temperature and drive level. This is why tunable circuits use a trimmer capacitor or an adjustable core: the calculation gets you close, and the adjustment closes the gap.
The Mechanical Analogy That Makes This Intuitive
An LC circuit is mathematically identical to a mass on a spring, and the correspondence is exact rather than merely poetic. Inductance plays the role of mass, resisting changes in current the way mass resists changes in velocity. The reciprocal of capacitance plays the role of spring stiffness. Resistance plays the role of friction, draining energy from the oscillation.
The spring formula ω = √(k/m) becomes ω = √(1/(LC)), which is the same equation this page solves. Energy sloshes between the magnetic field of the inductor and the electric field of the capacitor exactly as it sloshes between kinetic and potential energy in a spring. A damped oscillation dying away in a real LC circuit is the same phenomenon as a spring gradually coming to rest. If that analogy is useful, the Hooke's law calculator works the mechanical side of it.
For unit handling across this subject, use the inductance converter, the capacitance converter, the frequency converter and the resistance converter. For power and current questions in the surrounding circuit, the electrical power calculator covers the basics, and the free tools hub lists everything else.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Getting the metric prefix wrong — µH and mH differ by a thousand, and the resulting frequency by about thirty-two. Use the unit selectors rather than typing decimals.
- Ignoring stray capacitance — layout and inter-winding capacitance add to C and pull the resonance down, most noticeably at high frequencies where the design capacitance is small.
- Assuming series and parallel behave alike — they share a frequency formula but do the opposite thing at that frequency, one presenting minimum impedance and the other maximum.
- Forgetting the circulating current in a parallel tank — it can be Q times the supply current, so components must be rated for the internal current, not the external one.
- Treating Q as a property of the formula — it is a property of your actual components. Inductor loss usually dominates, so a good calculation cannot rescue a lossy coil.
Related Free Tools From Arb Digital
Unit work across this subject is handled by the inductance converter, the capacitance converter, the frequency converter and the resistance converter. For the surrounding circuit, see the electrical power calculator. For the mechanical analogue of resonance, the Hooke's law calculator, and for musical pitch frequencies the note frequency converter. The full set is on the free online tools hub.
Frequently Asked Questions
It is f equals one divided by two pi times the square root of L times C, with inductance in henries, capacitance in farads and the result in hertz. Rearranged, L equals one over four pi squared f squared C, and C equals one over four pi squared f squared L.
No, the resonant frequency is the same for both in the ideal lossless case. What differs is the behaviour at that frequency: a series circuit shows minimum impedance and maximum current, while a parallel circuit shows maximum impedance and minimum supply current.
Because only the product of L and C appears in the formula. What changes between those pairs is the characteristic impedance, the square root of L over C, which sets the voltage and current levels inside the tank and influences the Q factor.
It is the ratio of energy stored to energy lost per cycle, and it sets how sharply the circuit selects its resonant frequency. Bandwidth is the resonant frequency divided by Q, so a higher Q gives a narrower, more selective response.
Usually because of stray capacitance from board traces, inter-winding capacitance and the input capacitance of the following stage, all of which add to C. Component tolerance and the drift of capacitance with bias and temperature contribute as well.
It gives you the centre frequency, the characteristic impedance and the bandwidth, which is the starting point. A complete filter design also needs the source and load impedances and the required response shape, which this calculation does not address.
This page derives a frequency from physical component values using the resonance condition. A frequency converter only rescales an existing frequency between hertz, kilohertz, megahertz and similar units, with no circuit involved.
This tool is provided for educational and design-reference use. It models an idealised LC circuit and is not a substitute for measurement, simulation or compliance testing of a real electronic assembly.
