Last updated

Photopic (black) and scotopic [1] (green) luminosity functions. The photopic includes the CIE 1931 standard [2] (solid), the Judd–Vos 1978 modified data [3] (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data [4] (dotted). The horizontal axis is wavelength in nm.
General information
Unit system SI
Unit of luminous intensity
1 cd in ...... is equal to ...
   international candles   1.02 cp
   Hefner Kerze   1.11 HK

The candela ( /kænˈdɛlə/ or /kænˈdlə/ ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). [5] [6] It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the luminosity function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and ISO. [7] [4] [8] A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.


The word candela is Latin for candle. The old name "candle" is still sometimes used, as in foot-candle and the modern definition of candlepower . [9]


The 26th General Conference on Weights and Measures (CGPM) redefined the candela in 2018. [10] [11] The new definition, which took effect on 20 May 2019, is:

The candela [...] 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, which is equal to cd sr W−1, or cd sr kg−1 m−2 s3, where the kilogram, metre and second are defined in terms of h , c and ΔνCs.


Linear visible spectrum.svg

The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometres. The human eye, when adapted for bright conditions, is most sensitive near this frequency. Under these conditions, photopic vision dominates the visual perception of our eyes over the scotopic vision. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye. The luminous intensity for light of a particular wavelength λ is given by

where Iv(λ) is the luminous intensity, Ie(λ) is the radiant intensity and is the photopic luminosity function. If more than one wavelength is present (as is usually the case), one must integrate over the spectrum of wavelengths to get the total luminous intensity.



Prior to 1948, various standards for luminous intensity were in use in a number of countries. These were typically based on the brightness of the flame from a "standard candle" of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these was the English standard of candlepower. One candlepower was the light produced by a pure spermaceti candle weighing one sixth of a pound and burning at a rate of 120  grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp. [12]

A better standard for luminous intensity was needed. In 1884, Jules Violle had proposed a standard based on the light emitted by 1 cm2 of platinum at its melting point (or freezing point). The resulting unit of intensity, called the "violle", was roughly equal to 60 English candlepower. Platinum was convenient for this purpose because it had a high enough melting point, was not prone to oxidation, and could be obtained in pure form. [13] Violle showed that the intensity emitted by pure platinum was strictly dependent on its temperature, and so platinum at its melting point should have a consistent luminous intensity.

In practice, realizing a standard based on Violle's proposal turned out to be more difficult than expected. [13] Impurities on the surface of the platinum could directly affect its emissivity, and in addition impurities could affect the luminous intensity by altering the melting point. Over the following half century various scientists tried to make a practical intensity standard based on incandescent platinum. The successful approach was to suspend a hollow shell of thorium dioxide with a small hole in it in a bath of molten platinum. The shell (cavity) serves as a black body, producing black-body radiation that depends on the temperature and is not sensitive to details of how the device is constructed.

In 1937, the Commission Internationale de l'Éclairage (International Commission on Illumination) and the CIPM proposed a "new candle" based on this concept, with value chosen to make it similar to the earlier unit candlepower. The decision was promulgated by the CIPM in 1946:

The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new candles per square centimetre. [14]

It was then ratified in 1948 by the 9th CGPM [15] which adopted a new name for this unit, the candela. In 1967 the 13th CGPM removed the term "new candle" and gave an amended version of the candela definition, specifying the atmospheric pressure applied to the freezing platinum:

The candela is the luminous intensity, in the perpendicular direction, of a surface of 1/600000 square metre of a black body at the temperature of freezing platinum under a pressure of 101325 newtons per square metre. [16]

In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by radiometry, the 16th CGPM adopted a new definition of the candela: [17] [18]

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012  hertz and that has a radiant intensity in that direction of 1/683  watt per steradian.

The definition describes how to produce a light source that (by definition) emits one candela, but does not specify the luminosity function for weighting radiation at other frequencies. Such a source could then be used to calibrate instruments designed to measure luminous intensity with reference to a specified luminosity function. An appendix to the SI Brochure [19] makes it clear that the luminosity function is not uniquely specified, but must be selected to fully define the candela.

The arbitrary (1/683) term was chosen so that the new definition would precisely match the old definition. Although the candela is now defined in terms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition. [20]

The 26th CGPM approved the modern definition of the candela in 2018 as part of the 2019 redefinition of SI base units, which redefined the SI base units in terms of fundamental physical constants.

SI photometric light units

QuantityUnit Dimensions
[nb 1]
NameSymbol [nb 2] NameSymbol
Luminous energy Qv [nb 3] lumen second lm⋅sTJThe lumen second is sometimes called the talbot.
Luminous flux, luminous powerΦ v [nb 3] lumen (= candela steradian)lm (= cd⋅sr)JLuminous energy per unit time
Luminous intensity Iv candela (= lumen per steradian) cd (= lm/sr)JLuminous flux per unit solid angle
Luminance Lv candela per square metre cd/m2 (= lm/(sr⋅m2))L−2JLuminous 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−2JLuminous flux incident on a surface
Luminous exitance, luminous emittanceMvlumen per square metrelm/m2L−2JLuminous flux emitted from a surface
Luminous exposure Hv lux second lx⋅sL−2TJTime-integrated illuminance
Luminous energy densityωvlumen second per cubic metrelm⋅s/m3L−3TJ
Luminous efficacy (of radiation)Klumen per watt lm/W M−1L−2T3JRatio of luminous flux to radiant flux
Luminous efficacy (of a source)η [nb 3] lumen per watt lm/W M−1L−2T3JRatio of luminous flux to power consumption
Luminous efficiency, luminous coefficientV1Luminous efficacy normalized by the maximum possible efficacy
See also: SI  · Photometry  · Radiometry
  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. 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.

Relationships between luminous intensity, luminous flux, and illuminance

If a source emits a known luminous intensity Iv (in candelas) in a well-defined cone, the total luminous flux Φv in lumens is given by

where A is the radiation angle of the lamp—the full vertex angle of the emission cone. For example, a lamp that emits 590 cd with a radiation angle of 40° emits about 224 lumens. See MR16 for emission angles of some common lamps.

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12.6 lumens.

For the purpose of measuring illumination, the candela is not a practical unit, as it only applies to idealized point light sources, each approximated by a source small compared to the distance from which its luminous radiation is measured, also assuming that it is done so in the absence of other light sources. What gets directly measured by a light meter is incident light on a sensor of finite area, i.e. illuminance in lm/m2 (lux). However, if designing illumination from many point light sources, like light bulbs, of known approximate omnidirectionally uniform intensities, the contributions to illuminance from incoherent light being additive, it is mathematically estimated as follows. If ri is the position of the ith source of uniform intensity Ii, and â is the unit vector normal to the illuminated elemental opaque area dA being measured, and provided that all light sources lie in the same half-space divided by the plane of this area,

In the case of a single point light source of intensity Iv, at a distance r and normally incident, this reduces to

SI multiples

Like other SI units, the candela can also be modified by adding a metric prefix that multiplies it by a power of 10, for example millicandela (mcd) for 10−3 candela.

Related Research Articles

<span class="mw-page-title-main">Luminance</span> Photometric measure

Luminance is a photometric measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through, is emitted from, or is reflected from a particular area, and falls within a given solid angle.

<span class="mw-page-title-main">Caesium standard</span> Primary frequency standard

The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis Essen in 1955 at the National Physical Laboratory in the UK. and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.

<span class="mw-page-title-main">Lux</span> SI derived unit of illuminance

The lux is the unit of illuminance, or luminous flux per unit area, in the International System of Units (SI). It is equal to one lumen per square metre. In photometry, this is used as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface. It is analogous to the radiometric unit watt per square metre, but with the power at each wavelength weighted according to the luminosity function, a model of human visual brightness perception, standardized by the CIE and ISO. In English, "lux" is used as both the singular and plural form. The word is derived from the Latin word for "light", lux.

<span class="mw-page-title-main">Luminous efficiency function</span> Description of the average spectral sensitivity of human visual perception of brightness

A luminous efficiency function or luminosity function represents the average spectral sensitivity of human visual perception of light. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It is not an absolute reference to any particular individual, but is a standard observer representation of visual sensitivity of theoretical human eye. It is valuable as a baseline for experimental purposes, and in colorimetry. Different luminous efficiency functions apply under different lighting conditions, varying from photopic in brightly lit conditions through mesopic to scotopic under low lighting conditions. When not specified, the luminous efficiency function generally refers to the photopic luminous efficiency function.

In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human eye. The SI unit of luminous intensity is the candela (cd), an SI base unit.

<span class="mw-page-title-main">Photometry (optics)</span> Science of the measurement of visible light

Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power. In modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this weighting function is the photopic sensitivity function, although the scotopic function or other functions may also be applied in the same way. The weightings are standardized by the CIE and ISO.

<span class="mw-page-title-main">Foot-candle</span>

A foot-candle is a non-SI unit of illuminance or light intensity. The foot-candle is defined as one lumen per square foot. This unit is commonly used in lighting layouts in parts of the world where United States customary units are used, mainly the United States. Nearly all of the world uses the corresponding SI derived unit lux, defined as one lumen per square meter.

In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre (W⋅m−2). The CGS unit erg per square centimetre per second (erg⋅cm−2⋅s−1) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.

<span class="mw-page-title-main">Luminous flux</span> Perceived luminous power

In photometry, luminous flux or luminous power is the measure of the perceived power of light. It differs from radiant flux, the measure of the total power of electromagnetic radiation, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light.

<span class="mw-page-title-main">Illuminance</span> Luminous flux incident on a surface per area

In photometry, illuminance is the total luminous flux incident on a surface, per unit area. It is a measure of how much the incident light illuminates the surface, wavelength-weighted by the luminosity function to correlate with human brightness perception. Similarly, luminous emittance is the luminous flux per unit area emitted from a surface. Luminous emittance is also known as luminous exitance.

<span class="mw-page-title-main">Candlepower</span> Unit of measurement

Candlepower is a unit of measurement for luminous intensity. It expresses levels of light intensity relative to the light emitted by a candle of specific size and constituents. The historical candlepower is equal to 0.981 candelas. In modern usage, candlepower is sometimes used as a synonym for candela.

The lumen is the unit of luminous flux, a measure of the total quantity of visible light emitted by a source per unit of time, in the International System of Units (SI). Luminous flux differs from power in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model of the human eye's sensitivity to various wavelengths, this weighting is standardized by the CIE and ISO. One lux is one lumen per square metre.

In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiant intensity is the watt per steradian, while that of spectral intensity in frequency is the watt per steradian per hertz and that of spectral intensity in wavelength is the watt per steradian per metre —commonly the watt per steradian per nanometre. Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity.

<span class="mw-page-title-main">Spectral power distribution</span>

In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.

<span class="mw-page-title-main">Photosynthetically active radiation</span> Range of light usable for photosynthesis

Photosynthetically active radiation (PAR) designates the spectral range of solar radiation from 400 to 700 nanometers that photosynthetic organisms are able to use in the process of photosynthesis. This spectral region corresponds more or less with the range of light visible to the human eye. Photons at shorter wavelengths tend to be so energetic that they can be damaging to cells and tissues, but are mostly filtered out by the ozone layer in the stratosphere. Photons at longer wavelengths do not carry enough energy to allow photosynthesis to take place.

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 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.

The troland, named after Leonard T. Troland, is a unit of conventional retinal illuminance. It is meant as a method for correcting photometric measurements of luminance values impinging on the human eye by scaling them by the effective pupil size. It is equal to retinal illuminance produced by a surface whose luminance is one nit when the apparent area of the entrance pupil of the eye is 1 square millimeter.

<span class="mw-page-title-main">Jules Violle</span> French physicist (1841–1923)

Jules Louis Gabriel Violle was a French physicist and inventor.

In photometry, luminous energy is the perceived energy of light. This is sometimes called the quantity of light. Luminous energy is not the same as radiant energy, the corresponding objective physical quantity. This is because the human eye can only see light in the visible spectrum and has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to light at a wavelength of 555 nm. Light with a given amount of radiant energy will have more luminous energy if the wavelength is 555 nm than if the wavelength is longer or shorter. Light whose wavelength is well outside the visible spectrum has a luminous energy of zero, regardless of the amount of radiant energy present.

<span class="mw-page-title-main">Radiant flux</span> Radiant energy emitted, reflected, transmitted, or received per unit time

In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.


  1. "CIE Scotopic luminosity curve (1951)".
  2. "CIE (1931) 2-deg color matching functions".
  3. "Judd–Vos modified CIE 2-deg photopic luminosity curve (1978)".
  4. 1 2 Sharpe, Stockman, Jagla & Jägle (2005) 2-deg V*(l) luminous efficiency function Archived 27 September 2007 at the Wayback Machine
  5. International Bureau of Weights and Measures (20 May 2019), The International System of Units (SI) (PDF) (9th ed.), ISBN   978-92-822-2272-0, archived from the original on 18 October 2021
  6. CIE (2020). CIE S 017:2020 ILV: International Lighting Vocabulary, 2nd edition (2 ed.). CIE.
  7. ISO/CIE 23539:2023 CIE TC 2-93 Photometry — The CIE system of physical photometry. ISO/CIE. 2023. doi:10.25039/IS0.CIE.23539.2023.
  8. Wyzecki, G.; Stiles, W.S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley-Interscience. ISBN   0-471-02106-7.
  9. "Candlepower – Definition". Merriam-Webster Dictionary. Retrieved 15 February 2015.
  10. "Convocation of the General Conference on Weights and Measures (26th meeting)" (PDF). Versailles: Bureau International des Poids et Mesures. 13 November 2018. Archived from the original (PDF) on 19 September 2019. Retrieved 10 February 2019.
  11. BIPM (22 March 2021). "Mise en pratique for the definition of the candela in the SI". BIPM.
  12. "Hefner unit, or Hefner candle". 30 May 2007. Retrieved 25 February 2009.
  13. 1 2 Cottington, Ian E. (1986). "Platinum and the Standard of Light: A Selective Review of Proposals Which Led to an International Unit of Luminous Intensity". Platinum Metals Review. 30 (2): 84.
  14. Barry N. Taylor (1992). The Metric System: The International System of Units (SI). U. S. Department of Commerce. p. 18. ISBN   0-941375-74-9. (NIST Special Publication 330, 1991 ed.)
  15. Proceedings of the 9th CGPM, 1948, page 54 (French)
  16. 13th CGPM Resolution 5, CR, 104 (1967), and Metrologia, 4, 43–44 (1968).
  17. 16th CGPM Resolution 3, CR, 100 (1979), and Metrologia, 16, 56 (1980).
  18. "Base unit definitions: Candela". The NIST Reference on Constants, Units, and Uncertainty. Retrieved 27 September 2010.
  19. "Mise en pratique for the definition of the candela and associated derived units for photometric and radiometric quantities in the International System of Units (SI)". SI Brochure Appendix 2. Bureau International des Poids et Mesures. 22 March 2021. Retrieved 7 October 2023.
  20. "Units for photochemical and photobiological quantities". SI Brochure Appendix 3. Bureau International des Poids et Mesures. 22 March 2021. Retrieved 7 October 2023.