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# Lighting and Lumen Comparison and Conversion

Luminous efficacy is a figure of merit for light sources. It is the ratio of luminous flux (in lumens) to power (usually measured in watts). Depending on context, the power can be either the radiant flux of the source's output, or it can be the total electric power consumed by the source.  Which sense of the term is intended must usually be inferred from the context, and is sometimes unclear. The former sense is sometimes called luminous efficacy of radiation (LER), and the latter luminous efficacy of a source (LES).

The LES describes how well the source provides visible light from a given amount of electricity.  The LER is a characteristic of a given spectrum that describes how sensitive the human eye is to the mix of wavelengths involved. The luminous efficacy of a source is the LER of its emission spectrum times the conversion efficiency from electrical energy to electromagnetic radiation.

## Efficacy and efficiency

In some other systems of units, luminous flux has the same units as radiant flux. The luminous efficacy of radiation is then dimensionless. In this case, it is often instead called the luminous efficiency or luminous coefficient and may be expressed as a percentage. A common choice is to choose units such that the maximum possible efficacy, 683 lm/W, corresponds to an efficiency of 100%. The distinction between efficacy and efficiency is not always carefully maintained in published sources, so it is not uncommon to see "efficiencies" expressed in lumens per watt, or "efficacies" expressed as a percentage.

## Luminous efficacy of radiation

### Explanation

The response of a typical human eye to light, as standardized by the CIE in 1924. The horizontal axis is wavelength in nm

Wavelengths of light outside of the visible spectrum are not useful for illumination because they cannot be seen by the human eye. Furthermore, the eye responds more to some wavelengths of light than others, even within the visible spectrum. This response of the eye is represented by the luminosity function. This is a standardized function which represents the response of a "typical" eye under bright conditions (photopic vision). One can also define a similar curve for dim conditions (scotopic vision). When neither is specified, photopic conditions are generally assumed.

Luminous efficacy of radiation measures the fraction of electromagnetic power which is useful for lighting. It is obtained by dividing the luminous flux by the radiant flux. Light with wavelengths outside the visible spectrum reduces LER, because it contributes to the radiant flux while the luminous flux of such light is zero. Wavelengths near the peak of the eye's response contribute more strongly than those near the edges.

In SI, luminous efficacy has units of lumens per watt (lm/W). Photopic luminous efficacy of radiation has a maximum possible value of 683 lm/W, for the case of monochromatic light at a wavelength of 555 nm (green). Scotopic luminous efficacy of radiation reaches a maximum of 1700 lm/W for narrowband light of wavelength 507 nm.

### Mathematical definition

The dimensionless luminous efficiency measures the integrated fraction of the radiant power that contributes to its luminous properties as evaluated by means of the standard luminosity function.  The luminous coefficient is

$\frac{ \int^\infin_0 y_\lambda J_\lambda d\lambda } { \int^\infin_0 J_\lambda d\lambda },$

where

yλ is the standard luminosity function,
Jλ is the spectral power distribution of the radiant intensity.

The luminous coefficient is unity for a narrow band of wavelengths at 555 nanometres.

Note that $\int^\infin_0 y_\lambda J_\lambda d\lambda$ is an inner product between yλ and Jλ and that $\int^\infin_0 J_\lambda d\lambda$ is the one-norm of Jλ.

### Examples

Spectral radiance of a black body. Energy outside the visible wavelength range (~380–750 nm, shown by grey dotted lines) reduces the luminous efficiency.
Type

Luminous efficacy of radiation
(lm/W)
Luminous efficiency

Class M star (Antares, Betelgeuse), 3000 K 30 4%
ideal black-body radiator at 4000 K 47.5 7.0%
Class G star (Sun, Capella), 5800 K 80 12%
ideal black-body radiator at 7000 K 95 14%
ideal 5800 K black-body, truncated to 400–700 nm (ideal "white" source) 251 37%
ideal monochromatic 555 nm source 683 100%

## Lighting efficiency

Artificial light sources are usually evaluated in terms of luminous efficacy of a source, also sometimes called overall luminous efficacy. This is the ratio between the total luminous flux emitted by a device and the total amount of input power (electrical, etc.) it consumes. It is also sometimes referred to as the wall-plug luminous efficacy or simply wall-plug efficacy. The overall luminous efficacy is a measure of the efficiency of the device with the output adjusted to account for the spectral response curve (the “luminosity function”). When expressed in dimensionless form (for example, as a fraction of the maximum possible luminous efficacy), this value may be called overall luminous efficiency, wall-plug luminous efficiency, or simply the lighting efficiency.

The main difference between the luminous efficacy of radiation and the luminous efficacy of a source is that the latter accounts for input energy that is lost as heat or otherwise exits the source as something other than electromagnetic radiation. Luminous efficacy of radiation is a property of the radiation emitted by a source. Luminous efficacy of a source is a property of the source as a whole.

### Examples

The following table lists luminous efficacy of a source and efficiency for various light sources:

Category

Type

Overall
luminous efficacy (lm/W)
Overall
luminous efficiency
Combustion candle 0.3 0.04%
gas mantle 1–2 0.15–0.3%
Incandescent 100–200 W tungsten incandescent (220 V) 13.8–15.2 2.0–2.2%
100–200–500 W tungsten glass halogen (220 V) 16.7–17.6–19.8 2.4–2.6–2.9%
5–40–100 W tungsten incandescent (120 V) 5–12.6–17.5 0.7–1.8–2.6%
2.6 W tungsten glass halogen (5.2 V) 19.2 2.8%
tungsten quartz halogen (12–24 V) 24 3.5%
photographic and projection lamps 35 5.1%
Light-emitting diode white LED (raw, without power supply) 4.5–150 0.66–22.0%
4.1 W LED screw base lamp (120 V) 58.5–82.9 8.6–12.1%
6.9 W LED screw base lamp (120 V) 55.1–81.9 8.1–12.0%
7 W LED PAR20 (120 V) 28.6 4.2%
8.7 W LED screw base lamp (120 V) 69.0–93.1 10.1–13.6%
Arc lamp xenon arc lamp 30–50 4.4–7.3%
mercury-xenon arc lamp 50–55 7.3–8.0%
Fluorescent T12 tube with magnetic ballast 60 9%
9–32 W compact fluorescent 46–75 8–11.45%
T8 tube with electronic ballast 80–100 12–15%
T5 tube 70–104.2 10–15.63%
Gas discharge 1400 W sulfur lamp 100 15%
metal halide lamp 65–115 9.5–17%
high pressure sodium lamp 85–150 12–22%
low pressure sodium lamp 100–200 15–29%
Ideal sources Truncated 5800 K blackbody 251 37%
Green light at 555 nm (maximum possible LER) 683.002 100%

Sources that depend on thermal emission from a solid filament, such as incandescent light bulbs, tend to have low overall efficacy compared to an ideal blackbody source because, as explained by Donald L. Klipstein, “An ideal thermal radiator produces visible light most efficiently at temperatures around 6300 °C (6600 K or 11,500 °F). Even at this high temperature, a lot of the radiation is either infrared or ultraviolet, and the theoretical luminous [efficacy] is 95 lumens per watt. Of course, nothing known to any humans is solid and usable as a light bulb filament at temperatures anywhere close to this. The surface of the sun is not quite that hot. At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvins), most of its emission is in the infrared.

## SI photometry units

SI photometry units
QuantitySymbolSI unitAbbr.Notes
Luminous energy Qv lumen second lm·s units are sometimes called talbots
Luminous flux F lumen (= cd·sr) lm also called luminous power
Luminous intensity Iv candela (= lm/sr) cd an SI base unit
Luminance Lv candela per square metre cd/m2 units are sometimes called "nits"
Illuminance Ev lux (= lm/m2) lx Used for light incident on a surface
Luminous emittance Mv lux (= lm/m2) lx Used for light emitted from a surface
Luminous efficacy   lumen per watt lm/W ratio of luminous flux to radiant flux
See also SI · Photometry · Radiometry