Quality Factor (RLC)

Formula

Description

This form calculates Q directly from the component values of a series RLC circuit. The term √(L/C) has units of ohms and is called the characteristic impedance of the LC network. Q is then the ratio of this characteristic impedance to the series resistance. Lower resistance means less energy loss per cycle and higher Q. This formula reveals why component selection matters: for a given resonant frequency, you can trade off L and C values to achieve the desired Q while keeping f₀ = 1/(2π√(LC)) constant.

Variables

• Q — Quality factor (dimensionless)
• R — Series resistance in ohms (Ω)
• L — Inductance in henries (H)
• C — Capacitance in farads (F)

Practical Notes

For a parallel RLC circuit, the formula inverts to Q = R × √(C/L), because the parallel resistance damps the circuit differently. In real inductors, the series resistance (DCR) is the dominant loss mechanism that limits Q, which is why air-core inductors achieve higher Q than ferrite-core ones at high frequencies.