# 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. 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, and the latter luminous efficacy of a light source or overall luminous efficacy.
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.

## Luminous efficacy of radiation

By definition, light outside the visible spectrum cannot be seen by the standard human vision system, and therefore does not contribute to, and indeed can subtract from, luminous efficacy.

### Explanation

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 wavelengths outside the visible spectrum reduce luminous efficacy, because they contribute 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.
Wavelengths of light outside of the visible spectrum are not useful for general illumination. Furthermore, human vision responds more to some wavelengths of light than others. This response of the eye is represented by the luminous efficiency function. This is a standardized function representing photopic vision, which models the response of the eye's cone cells, that are active under typical daylight conditions. A separate curve can be defined for dark/night conditions, modeling the response of rod cells without cones, known as scotopic vision. (Mesopic vision describes the transition zone in dim conditions, between photopic and scotopic, where both cones and rods are active.)
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  . 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
    $K={\frac {\Phi _{\mathrm {v} }}{\Phi _{\mathrm {e} }}}={\frac {\int _{0}^{\infty }K(\lambda )\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }{\int _{0}^{\infty }\Phi _{\mathrm {e} ,\lambda }\,\mathrm {d} \lambda }},$
where
* Φ$_v$ is the luminous flux;
* Φ$_e$ is the radiant flux;
* Φ$_{e,λ}$ is the spectral radiant flux;
* K(λ) = K$_m$V(λ) is the spectral luminous efficacy.

### Examples
#### Photopic vision

| Type | Luminous efficacy of radiation (lm/W) | Luminous efficiency |
| Tungsten light bulb, typical, 2800 K | 15 | 2% |
| Class M star (Antares, Betelgeuse), 3300 K | 30 | 4% |
| Black body, 4000 K, ideal | 54.7 | 8% |
| Class G star (Sun, Capella), 5800 K | 93 | 13.6% |
| Black-body, 7000 K, ideal | 95 | 14% |
| Black-body, 5800 K, truncated to 400–700 nm (ideal "white" source) | 251 | 37% |
| Black-body, 5800 K, truncated to ≥ 2% photopic sensitivity range | 292 | 43% |
| Black-body, 2800 K, truncated to ≥ 2% photopic sensitivity range | 299 | 44% |
| Black-body, 2800 K, truncated to ≥ 5% photopic sensitivity range | 343 | 50% |
| Black-body, 5800 K, truncated to ≥ 5% photopic sensitivity range | 348 | 51% |
| Monochromatic source at 540 THz | 683 (exact) | 99.9997% |
| Ideal monochromatic source: 555 nm (in air) | 683.002 | 100% |

#### Scotopic vision

| Type | Luminous efficacy of radiation (lm/W) | Luminous efficiency |
| Ideal monochromatic 507 nm source | 1699 or 1700 | 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 |
| Combustion | Gas mantle | 1–2 | 0.15–0.3% |
| Incandescent | 15, 40, 100 W tungsten incandescent (230 V) | 8.0, 10.4, 13.8 | 1.2, 1.5, 2.0% |
| Incandescent | 5, 40, 100 W tungsten incandescent (120 V) | 5.0, 12.6, 17.5 | 0.7, 1.8, 2.6% |
| Halogen incandescent | 100, 200, 500 W tungsten halogen (230 V) | 16.7, 17.6, 19.8 | 2.4, 2.6, 2.9% |
| Halogen incandescent | 2.6 W tungsten halogen (5.2 V) | 19.2 | 2.8% |
| Halogen incandescent | Halogen-IR (120 V) | 17.7–24.5 | 2.6–3.5% |
| Halogen incandescent | Tungsten quartz halogen (12–24 V) | 24 | 3.5% |
| Halogen incandescent | Photographic and projection lamps | 35 | 5.1% |
| Light-emitting diode | LED screw base lamp (120 V) | 102 | 14.9% |
| Light-emitting diode | 5–16 W LED screw base lamp (230 V) | 75–217 | 11–32% |
| Light-emitting diode | 21.5 W LED retrofit for T8 fluorescent tube (230 V) | 172 | 25% |
| Light-emitting diode | Theoretical limit for a white LED with phosphorescence color mixing | 260–300 | 38.1–43.9% |
| Arc lamp | Carbon arc lamp | 2–7 | 0.29–1.0% |
| Arc lamp | Xenon arc lamp | 30–90 | 4.4–13.5% |
| Arc lamp | Mercury-xenon arc lamp | 50–55 | 7.3–8% |
| Arc lamp | Ultra-high-pressure (UHP) mercury-vapor arc lamp, free mounted | 58–78 | 8.5–11.4% |
| Arc lamp | Ultra-high-pressure (UHP) mercury-vapor arc lamp, with reflector for projectors | 30–50 | 4.4–7.3% |
| Fluorescent | 32 W T12 tube with magnetic ballast | 60 | 9% |
| Fluorescent | 9–32 W compact fluorescent (with ballast) | 46–75 | 8–11.45% |
| Fluorescent | T8 tube with electronic ballast | 80–100 | 12–15% |
| Fluorescent | PL-S 11 W U-tube, excluding ballast loss | 82 | 12% |
| Fluorescent | T5 tube | 70–104.2 | 10–15.63% |
| Fluorescent | 70–150 W inductively-coupled electrodeless lighting system | 71–84 | 10–12% |
| Gas discharge | 1400 W sulfur lamp | 100 | 15% |
| Gas discharge | Metal-halide lamp | 65–115 | 9.5–17% |
| Gas discharge | High-pressure sodium lamp | 85–150 | 12–22% |
| Gas discharge | Low-pressure sodium lamp | 100–200 | 15–29% |
| Gas discharge | Plasma display panel | 2–10 | 0.3–1.5% |
| Cathodoluminescence | Electron-stimulated luminescence | 30–110 | 15% |
| Ideal sources | Truncated 5800 K black-body | 251 | 37% |
| Ideal sources | Green light at 555 nm (maximum possible luminous efficacy by definition) | 683.002 | 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." At temperatures where the tungsten filament of an ordinary light bulb remains solid (below 3683 kelvin), most of its emission is in the infrared.

## SI photometry units

SI photometry quantitiesvte :
| Quantity | Quantity | Unit | Unit | Dimension | Notes |
| Name | Symbol | Name | Symbol | Dimension | Notes |
| Luminous energy | Q$_v$ | lumen second | lm⋅s | T⋅J | The lumen second is sometimes called the talbot. |
| Luminous flux, luminous power | Φ$_v$ | lumen (= candela steradian) | lm (= cd⋅sr) | J | Luminous energy per unit time |
| Luminous intensity | I$_v$ | candela (= lumen per steradian) | cd (= lm/sr) | J | Luminous flux per unit solid angle |
| Luminance | L$_v$ | candela per square metre | cd/m$^2$ (= lm/(sr⋅m$^2$)) | L$^{−2}$⋅J | Luminous flux per unit solid angle per unit projected source area. The candela per square metre is sometimes called the nit. |
| Illuminance | E$_v$ | lux (= lumen per square metre) | lx (= lm/m$^2$) | L$^{−2}$⋅J | Luminous flux incident on a surface |
| Luminous exitance, luminous emittance | M$_v$ | lumen per square metre | lm/m$^2$ | L$^{−2}$⋅J | Luminous flux emitted from a surface |
| Luminous exposure | H$_v$ | lux second | lx⋅s | L$^{−2}$⋅T⋅J | Time-integrated illuminance |
| Luminous energy density | ω$_v$ | lumen second per cubic metre | lm⋅s/m$^3$ | L$^{−3}$⋅T⋅J | |
| Luminous efficacy (of radiation) | K | lumen per watt | lm/W | M$^{−1}$⋅L$^{−2}$⋅T$^3$⋅J | Ratio of luminous flux to radiant flux |
| Luminous efficacy (of a source) | η | lumen per watt | lm/W | M$^{−1}$⋅L$^{−2}$⋅T$^3$⋅J | Ratio of luminous flux to power consumption |
| Luminous efficiency, luminous coefficient | V | | | 1 | Luminous efficacy normalized by the maximum possible efficacy |
| See also: SIPhotometryRadiometry ||||||
* ↑ 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.
* ↑ 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
* 1 2 3 Alternative symbols sometimes seen: W for luminous energy, P or F for luminous flux, and ρ for luminous efficacy of a source.