# 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 Kcd, 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 Kcd :

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

The effect of this definition is that one lumen per watt is exactly 1683 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