LC Resonance Calculator: Frequency, L, C & Q
Resonant frequency of an LC circuit, or the L or C for a target frequency, with reactance and impedance; add R for Q, bandwidth and −3 dB points.
Prefixes: p n u (µ) m k M G — 10u, 4.7n, 2u2, 100p, 13.56M. Lower-case m is milli, upper-case M is mega.
Checked against resonance and half-power points found numerically from the circuit impedance with scipy. Runs in your browser.
How to use
- Choose what to solve for: the resonant frequency, the inductance or the capacitance.
- Enter the two known values with prefixes such as 10u, 100p, 4k7 or 10.7M.
- Optionally add a resistance and choose series or parallel to see Q, bandwidth and the two −3 dB frequencies.
About this tool
ShowHide
An inductor and a capacitor together resonate at f0 = 1 / (2π√(LC)), where their reactances are equal and cancel. This calculator solves that for whichever value is missing — the frequency from L and C, or the inductance or capacitance needed to hit a target such as a 455 kHz or 10.7 MHz IF, a 13.56 MHz RFID antenna or a 50 Hz notch — and reports the angular frequency, period, the reactance of each part at resonance and the characteristic impedance √(L/C). Values take engineering prefixes: 10u, 4.7n, 2u2, 100p, 13.56M (lower-case m is milli, upper-case M mega). Add a resistance to get a real circuit's selectivity. For R in series with L and C, Q = √(L/C)/R and the bandwidth is R/(2πL); for R across a parallel tank, Q = R/√(L/C) and the bandwidth is 1/(2πRC). The two half-power frequencies are computed exactly rather than as f0 ± BW/2: they sit symmetrically on a logarithmic scale, with f1 · f2 = f0², so at low Q the lower one is much closer to f0 than the upper. What the ideal model leaves out matters in practice. A real inductor's winding resistance is in series with it, not across the tank, which shifts a parallel circuit's zero-phase frequency slightly below f0 (by the factor √(1 − R²C/L)); both parts have self-resonances and parasitics that dominate at high frequency; and component tolerance moves f0 with the square root — a 10 % capacitor error shifts the frequency by about 5 %. Trimmer capacitors or adjustable cores exist for that reason.
Frequently asked questions
What is the resonant frequency formula?
f0 = 1 / (2π√(LC)), with L in henries and C in farads. For example 10 µH with 100 pF resonates at 5.033 MHz. At that frequency the inductor's reactance 2πfL equals the capacitor's 1/(2πfC), and the two cancel.
How do series and parallel resonance differ?
A series LC has minimum impedance at resonance — ideally zero, in practice the series resistance — so it passes that frequency. A parallel LC tank has maximum impedance, so it blocks it or, in an oscillator or IF stage, selects it. The resonant frequency is the same formula for both.
What do Q and bandwidth mean here?
Q measures how sharply the circuit responds: the bandwidth between the half-power (−3 dB) points is f0/Q. A series circuit's Q rises as its resistance falls; a parallel tank's Q rises as the resistance across it rises. Without R the ideal circuit has infinite Q, so those outputs appear only when R is entered.
Why are the −3 dB points not equally spaced around f0?
They are symmetric on a logarithmic frequency scale: their product is exactly f0². For a high-Q circuit the difference from arithmetic symmetry is tiny, but at Q near 1 the upper point is noticeably further away than the lower one. The calculator gives both exactly.
Why does my real circuit resonate at a different frequency?
Component tolerance (often ±5–20 % for capacitors and inductors), stray capacitance of wiring and PCB traces, the inductor's own winding capacitance, and loss resistance all shift it. Because f0 depends on the square root of L·C, a 10 % error in either shifts the frequency by roughly 5 %.
Related tools
Reactance & Resonance Calculator
Find capacitive reactance (Xc), inductive reactance (XL), or the LC resonant frequency, with pF–F, nH–H and Hz–GHz unit pickers.
Science & Engineering
RC & RL Filter and Time Constant Calculator
Time constant, cutoff frequency, step response and low- or high-pass gain and phase of an RC or RL circuit, plus the time to reach a voltage.
Science & Engineering
Air-Core Coil Inductance Calculator
Inductance of a single-layer air-core coil from diameter, length and turns using Nagaoka's exact coefficient, or the turns needed for a target inductance.
Science & Engineering
Op-Amp Gain Calculator
Gain, dB, output voltage, input impedance and bandwidth of inverting, non-inverting and difference op-amp stages, or standard resistors for a target gain.
Science & Engineering
Solution Dilution Calculator
Apply C₁V₁ = C₂V₂ to find any unknown — the stock volume to take, the final volume, or either concentration — plus the amount of solvent to add.
Science & Engineering
555 Timer Calculator (Astable & Monostable)
Frequency, period, high and low time and duty cycle of a 555 astable, the pulse width of a monostable, or RA and RB for a target frequency with E24 values.
Science & Engineering