lumen per watt

SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

lumen per watt

lm W^‑1

luminous efficacy

kg^‑1 m^‑2 s³ cd

Definition

The lumen per watt, symbol lm W^‑1, is the SI coherent derived unit of luminous efficacy.

Luminous efficacy

Luminous efficacy is a measure of the brightness of a light source, as perceived by the human eye, relative to the light source’s radiant power. In effect it is the ratio of the luminous flux to radiant intensity.

Electromagnetic radiation of frequency 540 THz is in the green region of the visible spectrum. The human eye, when adapted for bright conditions, is most sensitive near this frequency. At other frequencies, a higher radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye.

The fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz, symbol K_cd, is defined as 683 when expressed in the unit lm W⁻¹.

$K_{cd} \mspace{6mu} = \mspace{4mu} 683 \mspace{6mu} \text{lm} \mspace{6mu} \text{W}{^{-1}}$

Inverting this relation gives an exact expression for the lumen per watt in terms of the SI defining constant K_cd :

$1 \mspace{6mu} \text{lm} \mspace{6mu} \text{W}{^{-1}} \mspace{4mu} = \mspace{4mu} \dfrac{K_{cd}}{683}$

The effect of this definition is that one lumen per watt is exactly ¹⁄₆₈₃ of the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz.

Photometry units

Name	Symbol	Quantity	Expressed in terms of SI base units	Expressed in terms of other SI units
candela	cd	luminous intensity	cd	lm/sr
lumen	lm	luminous flux	cd	cd sr
lux	lx	illuminance	m^-2 cd	lm/m²
candela per square metre	m^-2 cd	luminance	m^-2 cd	cd/m²
lumen second	lm s	luminous energy	s cd	lm s
lumen per watt	lm W^‑1	luminous efficacy	kg^‑1 m^‑2 s³ cd	lm/W