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LUX is a derived unit based on lumen, and lumen is a derived unit based on candela.
One lux is equal to one lumen per square meter, where 4π lumen is the total luminous flux of a light source of one candela of luminous intensity:
1 lux = 1 lumen/sq-m
As with other SI units, SI prefixes can be used, for example a kilolux (klx) is 1,000 lux.
A lumen defines the light energy emitted by a light source. LUX on the other hand defines the "light density" over a surface area and is effected by the structure of the light fixture. For example, a parabolic reflector concentrates the light emission of a light bulb and therefore increases the LUX output of the bulb.
The lumen rating of a light bulb is measured by the bulb manufacturer using a calibrated very expensive light measurement device. It is not possible for a bulb purchaser to measure or confirm the lumen output of a light bulb. On the other hand the lux value of a light fixture is easily measured with low cost lux meters.
When measuring light bulbs, the difference between the units lumen and lux is that lumins is the TOTAL OTUPUT of the light bulb whereas the lux takes into account the area over which the luminous flux is projected. Therefore the Lux output of a light source is dependant on the light modifier (reflector) designed to concentrate the light. A flux of 1000 lumen, concentrated into an area of one square meter, lights up that square meter with an luminance of 1000 lux. The same 1000 lumen, spread out over ten square meters, produces a dimmer luminance of only 100 lux. Mathematically, 1 lx = 1 lm/m2.
A single fluorescent light fixture with an output of 12000 lumen might light a residential kitchen with an luminance of 500 lux. To light a factory floor with area dozens of times that of the kitchen would require dozens of such fixtures. Lighting a larger area to the same level of lux requires a greater number of lumen.
Lux versus footcandle
One footcandle ≈ 10.764 lux. The footcandle (or lumen per square foot) is a non-SI unit of luminance. Like the BTU, it is mainly only in common use in the United States, particularly in construction-related engineering and in building codes. Because lux and footcandles are different units of the same quantity, it is perfectly valid to convert footcandles to lux and vice versa.
The name "footcandle" conveys "the illuminance cast on a surface by a one-candela source one foot away." As natural as this sounds, this style of name is now frowned upon, because the dimensional formula for the unit is not foot candela, but lumen/sq ft. Some sources do however note that the "lux" can be thought of as a "metre-candle" (i.e. the illuminance cast on a surface by a one-candela source one metre away). A source that is farther away provides less illumination than one that is close, so one lux is less illuminance than one footcandle. Since illuminance follows the inverse-square law, and since one foot = 0.3048 m, one lux = 0.30482 footcandle ≈ 1/10.764 footcandle.
In practical applications, as when measuring room illumination, it is very difficult to measure illuminance more accurately than 10%, and for many purposes it is quite sufficient to think of one footcandle as about ten lux.