# Lumen (unit)

Lumen
Unit systemSI derived unit
Unit ofLuminous flux
Symbollm
Unit conversions
1 lm in ...... is equal to ...
SI base units   1 lm = 1 cdsr.

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. 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 meter.

The lumen is defined in relation to the candela as

1 lm = 1 cdsr.

A full sphere has a solid angle of 4π steradians,[1] so a light source that uniformly radiates one candela in all directions has a total luminous flux of 1 cd × 4π sr = 4π cd⋅sr ≈ 12.57 lumens.[2]

## 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 4π lumens. If the source were partly covered by an ideal absorbing hemisphere, that system would radiate half as much luminous flux—only 2π 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, 1 lx = 1 lm/m2.

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.[3][4] Many compact fluorescent lamps and other alternative light sources are labelled as being equivalent to an incandescent bulb with a specific wattage. Below is a table that shows typical luminous flux for common incandescent bulbs and their equivalents.

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

On September 1, 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).[11] This change is a result of the EU's Eco-design Directive for Energy-using Products (EuP).[12] 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.[13]

## 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.[14] 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.[15] 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 degrees Celsius. 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".[16]

### 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.[17]

### 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 photometry 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 TJ The lumen second is sometimes called the talbot.
Luminous flux, luminous power Φv [nb 3] lumen (= candela steradians) 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 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 lux lx L−2J Luminous flux emitted from a surface
Luminous exposure Hv lux second lx⋅s L−2TJ Time-integrated illuminance
Luminous energy density ωv lumen second per cubic metre lm⋅s⋅m−3 L−3TJ
Luminous efficacy η [nb 3] lumen per watt lm/W M−1L−2T3J Ratio of luminous flux to radiant flux or power consumption, depending on context
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 suffix "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 or K for luminous efficacy.

## Notes and references

1. ^ "Lesson introduction to solid angles". Retrieved Oct 4, 2010.
2. ^ Bryant, Robert H. "Lumens, Illuminance, Foot-candles and bright shiny beads…". The LED Light. Retrieved Oct 4, 2010.
3. ^ "OSRAM Dulux Energisparepærer" (PDF). Osram.dk. Archived from the original (pdf) on March 1, 2012. Retrieved May 25, 2013.
4. ^ "Conventional CFLs". Energy Federation Incorporated. Archived from the original on 2008-10-14. Retrieved Dec 23, 2008.
5. ^ "Learn About Light Output : ENERGY STAR". Energystar.gov. Retrieved 2012-07-15.
6. ^ "LED Light Bulb Buying Guide". The Lightbulb Company. 11 August 2016. Retrieved 16 November 2017.
7. ^
8. ^ one example has been found, at URL: https://www.amazon.com/PacLights-Ultra150-Performance-Equivalent-Replacement/dp/B00F9CM49Y
9. ^ Philips Luxeon CoB emitters, specifically LHC1-4090-1208 datasheet http://www.philipslumileds.com/uploads/419/DS115-pdf
10. ^ Philips Luxeon CoB emitters, specifically LHC1-4090-1211 datasheet http://www.philipslumileds.com/uploads/419/DS115-pdf
11. ^ "Lighting now labelled in lumens". England: National Physical Laboratory. Retrieved March 10, 2012.
12. ^ "Ecodesign for energy-using appliances". Summaries of EU legislation. the EU institutions. Feb 2, 2010. Retrieved March 10, 2012.
13. ^ "Energy-saving light bulbs: how to read the packaging". European Commission. Archived from the original on 28 June 2013. Retrieved March 10, 2012.
14. ^ "ANSI lumen article". PC Magazine Encyclopedia. Retrieved Dec 20, 2006.
15. ^ "Projector Guide". CPILive.net. February 2004. Archived from the original on September 3, 2006. Retrieved Dec 20, 2006.
16. ^ "ANSI method of light output measurement". 1993. Archived from the original (doc) on February 26, 2012. Retrieved Jan 15, 2008.
17. ^ "Sony G70 Brochure" (PDF).