lumen

SI coherent derived unit with special name and symbol

Name

Symbol

Derived quantity

Expressed in terms of SI base units

lumen

luminous flux

Definition

The lumen, symbol lm, is the SI coherent derived unit of luminous flux,

One lumen is equal to the luminous flux emitted in a solid angle of one steradian by a uniform point source having a luminous intensity of one candela.

The lumen is defined in relation to the candela as:

$1 \ \text{lm} = 1 \ \text{cd} \ \text{sr}$

Luminous flux

Luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardised model of the sensitivity of the human eye across the visible range of the electromagnetic spectrum.

Luminous flux is a measure of the luminous energy emitted by a source, in all directions, per unit time. It can be thought of as the power, or brightness of a light source.

If a source radiating a power of one watt of monochromatic light, in the colour for which the eye is most efficient (a wavelength of 555 nm, in the green region of the optical spectrum), it will have a luminous flux of 683 lumens.

One lumen represents at least ¹⁄₆₈₃ watts of visible light power, depending on the spectral distribution.

Radiometry analogy

Luminous flux is analogous to radiant flux, the corresponding objective physical quantity used in the measurement science of radiometry.

Luminous flux differs from radiant flux in that radiant flux includes all frequencies of emitted electromagnetic waves, whereas luminous flux is weighted according to the human eye’s sensitivity to different electromagnetic wavelengths. Essentially, luminous flux is a measure of the visible component of a radiant flux.

Lumen vs candela

The difference between the units lumen and candela is that the candela describes the luminous flux in a particular direction, per unit solid angle, whereas the lumen describes the total luminous flux in all directions.

$1 \ \text{cd} = 1 \ \dfrac{\text{lm}}{\text{sr}}$


one candela = one lumen per steradian	one candela in all directions = a total luminous flux of 4π lumens

A complete sphere has a solid angle of 4π steradians. Therefore, a light source that uniformly radiates one candela (one lumen per steradian), in all directions has a total luminous flux of 4π lumens.

$1 \ \text{cd} \times 4\pi \ \text{sr} \ = \ 4\pi \ \text{cd} \ \text{sr} \ \approx \ 12.57 \ \text{lm}$

Lumen vs lux

The difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread.

A luminous flux of one lumen, concentrated onto an area of one square metre, lights that square metre with an illuminance of one lux. The same one lumen, spread out over ten square metres, produces a dimmer illuminance of 0.1 lux.

$1 \ \text{lx} = 1 \ \dfrac{\text{lm}} {\text{m}^2}$

Light bulbs

The sale of incandescent light bulbs has largely been replaced by energy-efficient light bulbs, including light bulbs using LED technologies. This has rendered meaningless the old method of comparing bulb brightnesses by their power consumption, measured in watts.

The lumen is now the standard unit used to describe the brightness of all domestic light bulbs, and is used alongside the power consumption in watts.

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