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Quality Factor (Series RLC)

The quality factor, or Q, measures how sharp and narrow the resonance peak of an RLC circuit is. A high Q means the circuit rings like a tuning fork, storing energy for many cycles before it dies out. A low Q means the resonance is broad and damped. Q is calculated as the resonant angular frequency times inductance divided by resistance. It is used in filters, oscillators, and radio tuning.

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AC Circuits Resonance
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Series RLC · Quality Factor

 Q = ω₀L / R
Q = ω₀L / R  ·  ω₀ = 1 / √(LC)
Series RLC resonance & quality factor
e.g. 10 Ω · 2.2 kΩ
e.g. 22 mH · 100 µH
e.g. 100 µF · 10 nF
V
optional · for current & voltage magnification
off‑resonance analysis
%
%
%
 Solve for
 Quick presets
 Select a target above — the calculator will solve for it using available inputs.
 Quality Factor
— (dimensionless)
 Resonant frequency
—
ω₀ = —
 Bandwidth
—
—
 Lower half-power
—
f₁
 Upper half-power
—
f₂
 XL at resonance
—Ω
inductive reactance
 XC at resonance
—Ω
capacitive reactance
 Circuit classification
—
based on Q
—
 Engineering interpretation
Calculate to see dynamic interpretation.
 Resonance behavior
Calculate to see resonance details.
ParameterLow QHigh Q
Resonancebroadsharp
Bandwidthwidenarrow
Selectivitylowerhigher
Dampinghigherlower
Frequency discriminationweakerstronger
f₀ f₁, f₂ (−3 dB) bandwidth region

 How to use this calculator

  • Enter series resistance, inductance, and capacitance with units.
  • Optionally add source voltage or operating frequency.
  • Click Calculate to see Q, resonance, and bandwidth.
  • Switch to Advanced mode for tolerances, solve‑for, and target design.
  • Use the presets to quickly explore common component values.
  • Review the graph and interpretation to understand circuit behavior.

 What this tool offers

  • Series RLC quality factor (Q) and resonant frequency
  • Angular resonant frequency, reactances, and bandwidth
  • Exact half‑power frequencies (f₁, f₂) with approximation note
  • Circuit classification & engineering interpretation
  • Off‑resonance impedance & phase analysis
  • Target component design (solve for R, L, C, f₀, BW)
  • Component tolerance estimates (worst‑case range)
  • Voltage magnification & resonant current
  • Interactive frequency‑response graph
  • Smart unit conversion & formatted engineering output

 Formula reference

Q = ω₀L / R quality factor
Q = 1 / (ω₀CR) alternate form
Q = (1/R)√(L/C) equivalent
ω₀ = 1 / √(LC) angular resonance
f₀ = 1 / (2π√LC) resonant frequency
BW = f₀ / Q bandwidth
BW = R / (2πL) bandwidth (alternate)
Xₗ = 2πfL inductive reactance
Xc = 1 / (2πfC) capacitive reactance
|Z| = √(R² + (Xₗ − Xc)²) impedance magnitude
Educational disclaimer: This calculator uses an idealized series RLC model. Real circuits are affected by inductor winding resistance, capacitor ESR, parasitic inductance and capacitance, component tolerances, frequency‑dependent losses, source impedance, skin effect, and dielectric losses. Always verify high‑frequency or high‑Q designs with datasheets, measurements, and circuit simulation.

Variables

Symbol Quantity Unit
Q Quality factor (series RLC) —
ω₀ Resonant angular frequency rad/s
L Inductance H
R Resistance Ω

What it means

The quality factor Q of a series RLC circuit at resonance is defined as Q = ω₀L / R, where ω₀ = 1/√(LC) is the resonant angular frequency. Alternatively, Q = 1/(R) * √(L/C). It measures the sharpness of the resonance: a high Q gives a narrow bandwidth and large voltage magnification across the inductor or capacitor at resonance. Q is also equal to the ratio of stored energy to energy dissipated per cycle. High‑Q circuits are used in oscillators, filters, and tuned amplifiers. In practical inductors, the Q is limited by winding resistance and core losses. Example: For L=0.1H, C=100µF, R=2Ω, ω₀ = 1/√(0.1*100e-6) = 316.2 rad/s. Then Q = (316.2*0.1)/2 = 31.62/2 = 15.8. The bandwidth is f₀/Q ≈ 50.3/15.8 ≈ 3.18 Hz, indicating a sharp resonance.

Worked example

Quality Factor – Practical Example

Real‑World
Scenario: A series RLC circuit has R = 50 Ω, L = 10 mH, and resonates at 1 kHz. Find the quality factor Q.
ParameterValue
R50 Ω
L10 mH
f₀1 kHz
FormulaQ = ω₀·L / R, ω₀ = 2πf₀
1ω₀ = 2π×1000 = 6283 rad/s
2Q = (6283 × 0.01) / 50 = 62.83 / 50 = 1.256
Final Design Q ≈ 1.26 ✓ Moderate sharpness
Why: Q indicates the sharpness of resonance – higher Q means a narrower bandwidth and larger voltage/current amplification.

Common mistakes

  • Resonant frequency ω₀: ω₀ = 1/√(LC) – natural frequency.
  • Q factor: Q = ω₀L/R – higher Q means sharper resonance.
  • Units: Q is dimensionless.
  • Bandwidth: BW = ω₀/Q (in rad/s) – related to the half‑power points.
  • Series RLC: This formula is for series resonance.

Applications

Quality factor Q of a series RLC circuit at resonance is Q = ω₀L/R, indicating the sharpness of the resonance peak. A higher Q means a narrower bandwidth and more selective filtering. Engineers use Q to design tuned circuits, to control the selectivity of filters, and to characterise oscillators. In communication systems, high‑Q circuits are used for channel selection. In power electronics, Q affects the damping of transients. By calculating Q, professionals can balance selectivity and bandwidth, ensuring that circuits meet performance specifications. This parameter is essential for resonant circuit design.

  • Band‑pass and notch filter design for communications
  • Tuned amplifier and oscillator circuit design
  • Antenna matching and impedance transformation
  • Inductor and capacitor selection for resonant circuits
  • Educational understanding of resonance and selectivity

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  • Published July 10, 2026
  • Last updated August 6, 2026