Lumen (unit)
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Lumen Unit

The lumen (symbol: lm) is the SI derived unit of luminous flux, a measure of the total quantity of visible light emitted by a source per unit of time. Luminous flux differs from power (radiant flux) in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model (a "luminosity function") of the human eye's sensitivity to various wavelengths. Lumens are related to lux in that one lux is one lumen per square metre.

## Definition

The 26th General Conference on Weights and Measures (CGPM) redefined the photometric units in 2018.[1] With the new definition, which took effect on 20 May 2019, the lumen

[...] is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressed in the unit lm W-1 [...]

Prior to 2019, the definition was based on the candela. The lumen is related to the candela as

1 lm = 1 cd ? sr.

A full sphere has a solid angle of 4? steradians,[2] so a light source that uniformly radiates one candela in all directions has a total luminous flux of .[3]

## Explanation

If a light source emits one candela of luminous intensity uniformly across a solid angle of one steradian, the total luminous flux emitted into that angle is one lumen (1 cd·1 sr = 1 lm). Alternatively, an isotropic one-candela light-source emits a total luminous flux of exactly 4? lumens. If the source were partly covered by an ideal absorbing hemisphere, that system would radiate half as much luminous flux—only 2? lumens. The luminous intensity would still be one candela in those directions that are not obscured.

The lumen can be thought of casually as a measure of the total amount of visible light in some defined beam or angle, or emitted from some source. The number of candelas or lumens from a source also depends on its spectrum, via the nominal response of the human eye as represented in the luminosity function.

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 flux of 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. The same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Mathematically, .

A source radiating a power of one watt of light in the color for which the eye is most efficient (a wavelength of 555 nm, in the green region of the optical spectrum) has luminous flux of 683 lumens. So a lumen represents at least 1/683 watts of visible light power, depending on the spectral distribution.

## Lighting

A standard LED lamp capable of producing 470 lumens. It consumes about one sixth the energy of an incandescent light bulb producing the same light.

Lamps used for lighting are commonly labelled with their light output in lumens; in many jurisdictions this is required by law.

A 23 W spiral compact fluorescent lamp emits about 1,400-1,600 lm.[4][5] Many compact fluorescent lamps and other alternative light sources are labelled as being equivalent to an incandescent bulb with a specific power. Below is a table that shows typical luminous flux for common incandescent bulbs and their equivalents.

Electrical power equivalents for different lamps[6][7][8]
Minimum light output (lumens) Electrical power consumption (watts)
Incandescent Compact fluorescent LED
Non-halogen Halogen
200 25 3-5 3
450 40 29 9-11 5-8
800 60 13-15 8-12
1,100 75 53 18-20 10-16
1,600 100 72 24-28 14-17
2,400 150 30-52 24-30[9]
3,100 200 49-75 32[10]
4,000 300 75-100 40.5[11]

On 1 September 2010, European Union legislation came into force mandating that lighting equipment must be labelled primarily in terms of luminous flux (lm), instead of electric power (W).[12] This change is a result of the EU's Eco-design Directive for Energy-using Products (EuP).[13] For example, according to the European Union standard, an energy-efficient bulb that claims to be the equivalent of a 60 W tungsten bulb must have a minimum light output of 700-750 lm.[14]

## Projector output

### ANSI lumens

The light output of projectors (including video projectors) is typically measured in lumens. A standardized procedure for testing projectors has been established by the American National Standards Institute, which involves averaging together several measurements taken at different positions.[15] For marketing purposes, the luminous flux of projectors that have been tested according to this procedure may be quoted in "ANSI lumens", to distinguish them from those tested by other methods. ANSI lumen measurements are in general more accurate than the other measurement techniques used in the projector industry.[16] This allows projectors to be more easily compared on the basis of their brightness specifications.

The method for measuring ANSI lumens is defined in the IT7.215 document which was created in 1992. First the projector is set up to display an image in a room at a temperature of 25 °C (77 °F). The brightness and contrast of the projector are adjusted so that on a full white field, it is possible to distinguish between a 5% screen area block of 95% peak white, and two identically sized 100% and 90% peak white boxes at the center of the white field. The light output is then measured on a full white field at nine specific locations around the screen and averaged. This average is then multiplied by the screen area to give the brightness of the projector in "ANSI lumens".[17]

### Peak lumens

Peak lumens is a measure of light output normally used with CRT video projectors. The testing uses a test pattern typically at either 10 and 20 percent of the image area as white at the center of the screen, the rest as black. The light output is measured just in this center area. Limitations with CRT video projectors result in them producing greater brightness when just a fraction of the image content is at peak brightness. For example, the Sony VPH-G70Q CRT video projector produces 1200 "peak" lumens but just 200 ANSI lumens.[18]

### Color light output

Brightness (white light output) measures the total amount of light projected in lumens. The color brightness specification Color Light Output measures red, green, and blue each on a nine-point grid, using the same approach as that used to measure brightness.

## SI photometric units

SI photometry quantities
Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol[nb 2]
Luminous energy Qv[nb 3] lumen second lm?s T J The lumen second is sometimes called the talbot.
Luminous flux, luminous power ?v[nb 3] lumen (= candela steradian) lm (= cd?sr) J Luminous energy per unit time
Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr) J Luminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 (= lm/(sr?m2)) L-2J Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit.
Illuminance Ev lux (= lumen per square metre) lx (= lm/m2) L-2J Luminous flux incident on a surface
Luminous exitance, luminous emittance Mv lumen per square metre lm/m2 L-2J Luminous flux emitted from a surface
Luminous exposure Hv lux second lx?s L-2T J Time-integrated illuminance
Luminous energy density ?v lumen second per cubic metre lm?s/m3 L-3T J
Luminous efficacy (of radiation) K lumen per watt lm/W M-1L-2T3J Ratio of luminous flux to radiant flux
Luminous efficacy (of a source) ?[nb 3] lumen per watt lm/W M-1L-2T3J Ratio of luminous flux to power consumption
Luminous efficiency, luminous coefficient V 1 Luminous efficacy normalized by the maximum possible efficacy
1. ^ Standards organizations recommend that photometric quantities be denoted with a subscript "v" (for "visual") to avoid confusion with radiometric or photon quantities. For example: USA Standard Letter Symbols for Illuminating Engineering USAS Z7.1-1967, Y10.18-1967
2. ^ The symbols in this column denote dimensions; "L", "T" and "J" are for length, time and luminous intensity respectively, not the symbols for the units litre, tesla and joule.
3. ^ a b c Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.

## Notes and references

1. ^ "Convocation of the General Conference on Weights and Measures (26th meeting)" (pdf). Versailles: Bureau International des Poids et Mesures. 13 November 2018.
2. ^ "Lesson introduction to solid angles". Retrieved 2010.
3. ^ Bryant, Robert H. "Lumens, Illuminance, Foot-candles and bright shiny beads...". The LED Light. Retrieved 2010.
4. ^ "OSRAM Dulux Energisparepærer" (PDF). Osram.dk. Archived from the original (PDF) on March 1, 2012. Retrieved 2013.
5. ^ "Conventional CFLs". Energy Federation Incorporated. Archived from the original on 2008-10-14. Retrieved 2008.
6. ^ "Learn About Light Output : ENERGY STAR". Energystar.gov. Retrieved .
7. ^ "LED Light Bulb Buying Guide". The Lightbulb Company. 11 August 2016. Retrieved 2017.
8. ^ "Halogen lamps". www.westinghouse.com. Westinghouse. Retrieved 2020.
9. ^ one example has been found, at URL: https://www.amazon.com/PacLights-Ultra150-Performance-Equivalent-Replacement/dp/B00F9CM49Y
10. ^ Philips Luxeon CoB emitters, specifically LHC1-4090-1208 datasheet http://www.philipslumileds.com/uploads/419/DS115-pdf
11. ^ Philips Luxeon CoB emitters, specifically LHC1-4090-1211 datasheet http://www.philipslumileds.com/uploads/419/DS115-pdf
12. ^ "Lighting now labelled in lumens". England: National Physical Laboratory. Retrieved 2012.
13. ^ "Ecodesign for energy-using appliances". Summaries of EU legislation. the EU institutions. Feb 2, 2010. Retrieved 2012.
14. ^ "Energy-saving light bulbs: how to read the packaging". European Commission. Archived from the original on 28 June 2013. Retrieved 2012.
15. ^ "ANSI lumen article". PC Magazine Encyclopedia. Retrieved 2006.
16. ^ "Projector Guide". CPILive.net. February 2004. Archived from the original on September 3, 2006. Retrieved 2006.
17. ^ "ANSI method of light output measurement". 1993. Archived from the original (doc) on February 26, 2012. Retrieved 2008.
18. ^ "Sony G70 Brochure" (PDF).