Q Factor Calculator
Quality factor of a resonator from bandwidth, from series/parallel RLC values or from energy decay — with damping ratio, ring-down time and half-power bandwidth.
How it works
Q = f₀ ÷ Δf₋₃dB = 2π · (energy stored ÷ energy lost per cycle); series RLC: Q = (1/R)√(L/C); parallel: Q = R√(C/L); ζ = 1/(2Q)
Q measures how sharply a system resonates: the ratio of stored to dissipated energy per radian, equivalently centre frequency over bandwidth. A tuning fork has Q in the thousands and rings for seconds; an audio filter with Q = 1 is broad and dies within a cycle. In a series RLC circuit resistance spoils Q; in a parallel tank it is the shunt loss that matters, so the formulas invert. Q also sets how many cycles a transient takes to decay — roughly Q/π to fall to 1/e.
Worked example
A 1 MHz filter 20 kHz wide has Q = 50, damping ratio 0.01, loses 12.6% of its energy per cycle and rings for about 73 cycles before settling to 1%.
Frequently asked questions
What Q is “high”?
Above about 10 the approximations here are accurate; crystals reach 10⁴–10⁶, superconducting cavities 10¹⁰.
How do loaded and unloaded Q differ?
Connecting a source and load adds loss; loaded Q is always lower and is what a filter actually exhibits in circuit.
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This calculator is for educational purposes. Double-check important results before acting on them.