Why use tolerance and sweep features?

Tolerance range helps estimate resonance drift from real component variation. Sweep summary helps you see where impedance is lowest/highest around an operating region, useful for tuning filters and resonant networks.

What is Q factor and why does it matter?

Q factor (Quality Factor) measures how underdamped a resonant circuit is. A high Q means the circuit resonates sharply with low energy loss, as a narrow-band filter needs. A low Q means a broader, more lossy response. Q = f_resonant / Bandwidth. This calculator computes Q from your L, C, resistance and ESR.

How do I calculate an LC tank circuit?

Set Circuit Type to Parallel RLC, enter your inductor and capacitor values, and the resonant frequency comes straight out of f = 1/(2π√(LC)): the frequency the tank oscillates at. Q and bandwidth appear as soon as there is a loss to set them. Enter the coil's series resistance as ESR, under Frequency Sweep & Parasitics, rather than in R: in a parallel tank R is a resistance across it, such as its load, and the coil's loss is converted to its equivalent across the tank, L ÷ (C × ESR). This tool models the coil's loss (ESR); a capacitor's own loss is not modeled. Switch the solver to Impedance to see how high the impedance peaks at resonance, and its phase.

What frequency will my LC oscillator run at?

The resonant frequency of its LC network, which is what this calculator solves for. Enter the inductance and capacitance and read the frequency: a 100 μH coil with 10 nF gives 159.155 kHz. One practical caveat the tool shows you: real components are not their printed values, so open Component Tolerance Analysis to see the frequency band a 5% part actually lands in. One it cannot: stray capacitance in the layout adds to C, pulling the frequency down rather than up, and that is not modeled here.

Can this handle an RLC circuit, not just LC?

Yes. Circuit Type offers RLC Circuit (Series) and RLC Circuit (Parallel), also written LCR or RCL, alongside plain LC. Resistance does not move the resonant frequency, which depends only on L and C, but it changes everything about how the circuit behaves there: it sets the impedance at resonance, and it sets Q and therefore bandwidth. Choose one of the RLC types, or add ESR, and Q and bandwidth are reported in every solve mode. They are omitted for a plain LC with no ESR, because an ideal lossless circuit has infinite Q, which is not a useful number.

Is a tuned circuit the same as a tank circuit?

They describe the same LC pair, also called an LC resonator, from different angles. "Tuned circuit" says what it is for, picking out one frequency, and "tank circuit" says how it does it, by storing and exchanging energy. The parallel arrangement is called a tank and the series one a tuned or acceptor circuit, because a series RLC does the opposite at resonance: minimum impedance instead of maximum. Both are covered here; pick the arrangement that matches your schematic.

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

Resonant frequency is f = 1 / (2π√(LC)), where L is inductance in henries and C is capacitance in farads. For a 100 µH inductor and a 100 nF capacitor, resonance is about 50.3 kHz. Enter any two of frequency, L, or C above and the calculator solves for the third, with optional standard-value snapping under Component Tolerance Analysis.

LC Circuit Calculator - Resonant Frequency & Q

Parameters

Calculate LC and RLC resonant frequency, impedance, Q factor, and bandwidth. Includes component tolerance analysis, E-series value snap, and an impedance sweep.

Select what to solve for

Enter known values

Set resistance (optional)

View results

The resonant frequency comes from the ideal L and C values. Resistance and ESR set Q, bandwidth and impedance here but do not move it, stray capacitance is not modeled, and real parts drift from their labelled values. Measure the built circuit before treating this number as final. At series resonance the voltage across the coil and the capacitor is about Q times the source voltage, so rate both parts for it.

Formulas and sources

Each formula this calculator uses, where it comes from, and what it leaves out. "How it works" shows the same formula with your own numbers.

Resonant frequency

Resonant Frequency mode

f = 1 ÷ (2π√(Inductance× Capacitance))

f: resonant frequency, in hertz
Inductance: L, in henries
Capacitance: C, in farads

The frequency of an ideal L and C. Resistance and coil loss change how sharp the resonance is, not where it falls; stray capacitance, which lowers it, is not modeled.

Source: Standard formula; no single publisher.

Inductance for a frequency

Inductance mode

Inductance = 1 ÷ ((2πf)² × Capacitance)

Inductance: L, in henries
f: target frequency, in hertz
Capacitance: C, in farads

Source: Standard formula, the line above solved for L; no single publisher.

Capacitance for a frequency

Capacitance mode

Capacitance = 1 ÷ ((2πf)² × Inductance)

Capacitance: C, in farads
f: target frequency, in hertz
Inductance: L, in henries

Source: Standard formula, the resonance line solved for C; no single publisher.

Impedance, LC (ideal)

Impedance mode, for LC Circuit (Ideal)

Impedance = j(X_L - X_C)

Impedance: Z, a complex number

Pure reactance: zero at resonance.

Source: Standard formula; no single publisher.

Impedance, series RLC

Impedance mode, for RLC Circuit (Series)

Impedance = R + j(X_L - X_C)

Impedance: Z, a complex number
R: series resistance plus the coil's ESR

Source: Standard formula; no single publisher.

Impedance, parallel RLC

Impedance mode, for RLC Circuit (Parallel)

Impedance = 1 / Y (parallel RLC)

Impedance: Z, a complex number
Y: the admittance across the tank: 1/R, plus the coil branch (ESR + jX_L) and the capacitor

A lossless tank at resonance has no finite impedance, and none is shown.

Source: Standard formula; no single publisher.

Reactances

Impedance mode

X_L = 2πfL X_C = 1 ÷ (2πfC)

Taken at the operating frequency you set, or at resonance when you set none.

Source: Standard formulas; no single publisher.

Q and bandwidth

With resistance or ESR

Q = √(L/C) ÷ (R + ESR) Q = R_tank ÷ √(L/C) Bandwidth = f ÷ Q

Q: quality factor
R_tank: R in parallel with L ÷ (C × ESR), the coil's loss seen across the tank
f: resonant frequency

The first line is a series circuit, the second a parallel tank. Turning the coil's ESR into a resistance across the tank is the high-Q approximation.

Source: Standard formulas; no single publisher.

Tolerance spread

With Component Tolerance Analysis open

f low = 1 ÷ (2π√(L(1 + tL) × C(1 + tC))) f high = 1 ÷ (2π√(L(1 - tL) × C(1 - tC)))

tL: the inductor's tolerance, as a fraction
tC: the capacitor's tolerance, as a fraction

Snapping picks the nearest E6, E12 or E24 value by ratio, in the value's own decade and one either side, and reports the frequency those parts give.

Source: Standard formula; no single publisher. Snapping uses the E6, E12 and E24 series named in IEC 60063:2015 [1], which this page did not read. The nearest-by-ratio rule is CalcTrail's own; no publisher.

Sources

International Electrotechnical Commission (IEC). IEC 60063:2015, Preferred number series for resistors and capacitors. Edition 3.0, March 27, 2015.

What this calculator does not cover

This treats L and C as ideal parts with one loss, the coil's ESR. It does not model stray or self capacitance, a capacitor's own loss, core saturation, mutual coupling, or how losses shift the resonant frequency of a heavily damped circuit.

Sources checked on October 5, 2026.

Help

Select what to solve for: Find the resonant frequency, the inductance or the capacitance, or choose Impedance to analyse a circuit you already have.
Enter known values: Enter the two values you know: inductance, capacitance or the target frequency.
Set resistance (optional): Choose Series or Parallel RLC and enter the resistance in line with L and C, or across them. Add the coil's own loss as ESR if you know it.
View results: See the value you solved for, with Q and bandwidth whenever there is resistance or ESR.

Understanding LC Circuits

What resonance means

An inductor and a capacitor exchange stored energy back and forth. At one frequency, the resonant frequency, their inductive and capacitive reactances (X_L and X_C) are equal and cancel, so the circuit behaves very differently there than at any other frequency. For an ideal L and C, this resonant frequency is also the natural (undamped) frequency: the rate at which the energy swaps with no drive.

Series vs. parallel: opposite behavior at resonance

A series circuit's impedance is lowest at resonance, so current peaks. A parallel tank's is highest, so the current drawn from the source is at its lowest. Same formula for frequency, opposite effect on the circuit.

The LC tank circuit

A tank circuit is an inductor and a capacitor wired in parallel, and the name is literal: energy sloshes between the two like liquid in a tank. The coil's magnetic field charges the capacitor, and the capacitor discharges back through the coil. At resonance the exchange needs only enough drive to replace its losses, and the tank's impedance peaks. Select Parallel RLC to see the tank's Q and bandwidth beside its resonant frequency, and solve for impedance to see how high its impedance peaks. The higher the Q, the narrower the peak.

Quality factor and bandwidth

Q factor measures how sharply the circuit responds around resonance: a higher Q means a narrower bandwidth, and a circuit more selective but less forgiving of component drift. A Q of 50 at 1 MHz gives a response band 20 kHz wide. Bandwidth here is the half-power (−3 dB) width of the response, f ÷ Q.

Why component tolerance matters

Real inductors and capacitors are never exactly the value printed on them. One part 5% off moves resonance by about 2.5%, and both parts 5% off move it by about 5%. Expand Component Tolerance Analysis to see the resulting frequency range across your parts' tolerance band. It can also snap your calculated values to the nearest E6, E12 or E24 value (IEC 60063 preferred values, with 6, 12 or 24 steps a decade). Snapping also reports the frequency those parts give and the error it introduces, and warns when the standard value moves you further than the components' own tolerance does.

Where this shows up in practice

Radio tuners, RF and antenna matching networks, oscillators, and low-pass, high-pass and bandpass filters all rely on the same LC resonance math. When solving for impedance, the sweep summary shows how the circuit behaves either side of the operating frequency you set, or either side of resonance when you set none.

Frequently Asked Questions

Both are optional, expandable sections on the same screen, not separate modes. Component Tolerance Analysis estimates resonance drift from real component variation and snaps values to the E6, E12 or E24 series of IEC 60063. Frequency Sweep & Parasitics adds the coil’s ESR, which lowers Q in every solve mode, and, when solving for impedance, a sweep summary of where the impedance is lowest and highest around the operating point.

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Last updated October 12, 2026

LC Circuit Calculator - Resonant Frequency & Q

Formulas and sources

Resonant frequency

Inductance for a frequency

Capacitance for a frequency

Impedance, LC (ideal)

Impedance, series RLC

Impedance, parallel RLC

Reactances

Q and bandwidth

Tolerance spread

Sources

What this calculator does not cover

Help

Quick Start Guide

Understanding LC Circuits

What resonance means

Series vs. parallel: opposite behavior at resonance

The LC tank circuit

Quality factor and bandwidth

Why component tolerance matters

Where this shows up in practice

Features

Common Use Cases

Frequently Asked Questions

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