# Luminous efficacy

Luminous efficacy is a measure of how well a light source produces visible light. It is the ratio of luminous flux to power, measured in lumens per watt in the International System of Units (SI). Depending on context, the power can be either the radiant flux of the source's output, or it can be the total power (electric power, chemical energy, or others) consumed by the source.[1][2][3] 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,[4] and the latter luminous efficacy of a light source[5] or overall luminous efficacy.[6][7]

Luminous efficacy
Common symbols
K
SI unitlm⋅W−1
In SI base unitscd⋅s3⋅kg−1⋅m−2
Dimension${\displaystyle {\mathsf {J}}{\mathsf {T}}^{3}{\mathsf {M}}^{-1}{\mathsf {L}}^{-2}}$

Not all wavelengths of light are equally visible, or equally effective at stimulating human vision, due to the spectral sensitivity of the human eye; radiation in the infrared and ultraviolet parts of the spectrum is useless for illumination. The luminous efficacy of a source is the product of how well it converts energy to electromagnetic radiation, and how well the emitted radiation is detected by the human eye.

## Efficacy and efficiency

Luminous efficacy can be normalized by the maximum possible luminous efficacy to a dimensionless quantity called luminous efficiency. 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.

### Explanation

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.[4] Light with wavelengths outside the visible spectrum reduces luminous efficacy, 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.

Photopic luminous efficacy of radiation has a maximum possible value of 683.002 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 monochromatic light at a wavelength of 507 nm.

### Mathematical definition

Luminous efficacy (of radiation), denoted K, is defined as[4]

${\displaystyle K={\frac {\Phi _{\mathrm {v} }}{\Phi _{\mathrm {e} }}}={\frac {\int _{0}^{\infty }K(\lambda )\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }{\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }},}$

where

### Examples

#### Photopic vision

Type Luminous efficacy
Luminous
efficiency[note 1]
Tungsten light bulb, typical, 2800 K 15[9] 2%
Class M star (Antares, Betelgeuse), 3300 K 30 4%
Black body, 4000 K, ideal 54.7[note 2] 8%
Class G star (Sun, Capella), 5800 K 93[9] 13.6%
Black-body, 7000 K, ideal 95[note 2] 14%
Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source)[note 3] 251[9][note 4][10] 37%
Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range[note 5] 292[10] 43%
Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range[note 5] 299[10] 44%
Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range[note 6] 343[10] 50%
Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range[note 6] 348[10] 51%
Ideal monochromatic source: 555 nm 683.002[11] 100%

#### Scotopic vision

Type Luminous efficacy

Luminous

efficiency[note 1]

Ideal monochromatic 507 nm source 1699[12] or 1700[13] 100%

## Lighting efficiency

Artificial light sources are usually evaluated in terms of luminous efficacy of the source, also sometimes called wall-plug 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. The luminous efficacy of the source 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 luminous efficiency of a source, overall luminous efficiency or 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. Note that all lamps requiring electrical/electronic ballast are unless noted (see also voltage) listed without losses for that, reducing total efficiency.

Category Type Overall luminous
efficacy (lm/W)
Overall luminous
efficiency[note 1]
Combustion Gas mantle 1–2[14] 0.15–0.3%
Incandescent 15, 40, 100 W tungsten incandescent (230 V) 8.0, 10.4, 13.8[15][16][17][18] 1.2, 1.5, 2.0%
5, 40, 100 W tungsten incandescent (120 V) 5.0, 12.6, 17.5[19] 0.7, 1.8, 2.6%
Halogen incandescent 100, 200, 500 W tungsten halogen (230 V) 16.7, 17.6, 19.8[20][18] 2.4, 2.6, 2.9%
2.6 W tungsten halogen (5.2 V) 19.2[21] 2.8%
Halogen-IR (120 V) 17.7–24.5[22] 2.6–3.5%
Tungsten quartz halogen (12–24 V) 24 3.5%
Photographic and projection lamps 35[23] 5.1%
Light-emitting diode LED screw base lamp (120 V) 102[24][25][26] 14.9%
5–16 W LED screw base lamp (230 V) 75–210[27][28] 11–30%
21.5 W LED retrofit for T8 fluorescent tube (230 V) 172[29] 25%
Theoretical limit for a white LED with phosphorescence color mixing 260–300[30] 38.1–43.9%
Arc lamp Carbon arc lamp 2–7[31] 0.29–1.0%
Xenon arc lamp 30–90[32][33][34] 4.4–13.5%
Mercury-xenon arc lamp 50–55[32] 7.3–8%
Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted 58–78[35] 8.5–11.4%
Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors 30–50[36] 4.4–7.3%
Fluorescent 32 W T12 tube with magnetic ballast 60[37] 9%
9–32 W compact fluorescent (with ballast) 46–75[18][38][39] 8–11.45%[40]
T8 tube with electronic ballast 80–100[37] 12–15%
PL-S 11 W U-tube, excluding ballast loss 82[41] 12%
T5 tube 70–104.2[42][43] 10–15.63%
70–150 W inductively-coupled electrodeless lighting system 71–84[44] 10–12%
Gas discharge 1400 W sulfur lamp 100[45] 15%
Metal-halide lamp 65–115[46] 9.5–17%
High-pressure sodium lamp 85–150[18] 12–22%
Low-pressure sodium lamp 100–200[18][47][48] 15–29%
Plasma display panel 2–10[49] 0.3–1.5%
Cathodoluminescence Electron-stimulated luminescence 30–110[50][51] 15%
Ideal sources Truncated 5800 K black-body[note 4] 251[9] 37%
Green light at 555 nm (maximum possible luminous efficacy by definition) 683.002[11] 100%

Sources that depend on thermal emission from a solid filament, such as incandescent light bulbs, tend to have low overall efficacy 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. No substance 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."[23] At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.[23]

## SI photometry units

Quantity Unit Dimension
[nb 1]
Notes
Name Symbol[nb 2] Name Symbol
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 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−2TJ Time-integrated illuminance
Luminous energy density ωv lumen second per cubic metre lm⋅s/m3 L−3TJ
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) η[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. ^ 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.
2. ^ 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
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

1. ^ a b c Defined such that the maximum possible luminous efficacy corresponds to a luminous efficiency of 100%.
2. ^ a b Black body visible spectrum
3. ^ Most efficient source that mimics the solar spectrum within range of human visual sensitivity.
4. ^ a b Integral of truncated Planck function times photopic luminosity function times 683.002 lm/W.
5. ^ a b Omits the part of the spectrum where the eye's sensitivity is very poor.
6. ^ a b Omits the part of the spectrum where the eye's sensitivity is low (≤ 5% of the peak).

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