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The candela ( or ; symbol: cd) is the unit of luminous intensity in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI). It measures luminous power per unit
solid angle In geometry, a solid angle (symbol: ) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point. The po ...
emitted by a light source in a particular direction. Luminous intensity is analogous to
radiant intensity 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 ta ...
, 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 standard
luminosity function 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 ...
(a model of the sensitivity of the human eye to different wavelengths). 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 A foot-candle (sometimes foot candle; abbreviated fc, lm/ft2, or sometimes ft-c) 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 par ...
'' and the modern definition of '' candlepower''.

# Definition

The 26th General Conference on Weights and Measures (CGPM) redefined the candela in 2018. 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, ''K''cd, to be 683 when expressed in the unit lm W−1, which is equal to , or , where the kilogram, metre and second are defined in terms of '' h'', '' c'' and Δ''ν''Cs.

## Explanation

The frequency chosen is in the
visible spectrum The visible spectrum is the portion of the electromagnetic spectrum that is visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' or simply light. A typical human eye will respond to wav ...
near
green Green is the color between cyan and yellow on the visible spectrum. It is evoked by light which has a dominant wavelength of roughly 495570 nm. In subtractive color systems, used in painting and color printing, it is created by a combina ...
, corresponding to a wavelength of about 555 nanometres. The
human eye The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm. T ...
, when
adapted In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
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 In the study of human visual perception, scotopic vision (or scotopia) is the vision of the eye under low-light conditions. The term comes from Greek ''skotos'', meaning "darkness", and ''-opia'', meaning "a condition of sight". In the human ey ...
. 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 :$I_\mathrm\left(\lambda\right)= 683.002\ \mathrm \cdot \overline\left(\lambda\right) \cdot I_\mathrm\left(\lambda\right) ,$ where ''I''v(''λ'') is the luminous intensity, ''I''e(''λ'') is the
radiant intensity 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 ta ...
and $\textstyle \overline\left(\lambda\right)$ is the
photopic Photopic vision is the vision of the eye under well-lit conditions (luminance levels from 10 to 108  cd/m2). In humans and many other animals, photopic vision allows color perception, mediated by cone cells, and a significantly higher visu ...
luminosity function 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 ...
. If more than one wavelength is present (as is usually the case), one must integrate over the
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
of wavelengths to get the total luminous intensity.

## Examples

*A common candle emits light with roughly 1 cd luminous intensity. *A 25 W compact fluorescent light bulb puts out around 1700  lumens; if that light is radiated equally in all directions (i.e. over 4
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radia ...
s), it will have an intensity of $I_\text = \frac \approx 135\ \text/\text = 135\ \text.$ *Focused into a 20° beam (0.095 steradians), the same light bulb would have an intensity of around 18,000 cd within the beam.

# History

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 Spermaceti is a waxy substance found in the head cavities of the sperm whale (and, in smaller quantities, in the oils of other whales). Spermaceti is created in the spermaceti organ inside the whale's head. This organ may contain as much as of ...
candle weighing one sixth of a pound and burning at a rate of 120
grains A grain is a small, hard, dry fruit ( caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legum ...
per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp. It became clear that a better-defined unit was needed. Jules Violle had proposed a standard based on the light emitted by 1 cm2 of
platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Platinum ...
at its melting point (or freezing point), calling this the Violle. The light intensity was due to the Planck radiator (a
black body A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body ...
) effect, and was thus independent of the construction of the device. This made it easy for anyone to measure the standard, as high-purity platinum was widely available and easily prepared. The '' Commission Internationale de l'Éclairage'' (International Commission on Illumination) and the CIPM proposed a "new candle" based on this basic concept. However, the value of the new unit was chosen to make it similar to the earlier unit candlepower by dividing the Violle by 60. 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.
It was then ratified in 1948 by the 9th CGPM 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 square metre of a black body at the temperature of freezing platinum under a pressure of  newtons per square metre.
In 1979, because of the difficulties in realizing a Planck radiator at high temperatures and the new possibilities offered by
radiometry Radiometry is a set of techniques for measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power in space, as opposed to photometric techniques, which cha ...
, the 16th CGPM adopted a new definition of the candela:
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency and that has a
radiant intensity 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 ta ...
in that direction of
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James Wat ...
per
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radia ...
.
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 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 The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...
(an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition. The 26th CGPM approved the modern definition of the candela in 2018 as part of the
2019 redefinition of SI base units In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144t ...
, which redefined the SI base units in terms of fundamental physical constants.

# SI photometric light units

## Relationships between luminous intensity, luminous flux, and illuminance

If a source emits a known luminous intensity ''I''v (in candelas) in a well-defined cone, the total luminous flux ''Φ''v in lumens is given by :''Φ''''v'' = ''I''''v'' 2  − cos(''A''/2) 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 4: 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 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 brightne ...
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 In physics, two wave sources are coherent if their frequency and waveform are identical. Coherence is an ideal property of waves that enables stationary (i.e., temporally or spatially constant) interference. It contains several distinct concepts ...
being additive, it is mathematically estimated as follows. If r''i'' is the position of the ''i''th 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, :$\text \mathbf\text dA\text E_\mathrm v\left(\mathbf\right) = \sum _.$ In the case of a single point light source of intensity ''Iv'', at a distance ''r'' and normally incident, this reduces to :$E_ \mathrm v\left(r\right) = \frac.$

# SI multiples

Like other SI units, the candela can also be modified by adding a
metric prefix A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
that multiplies it by a
power of 10 A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The f ...
, for example millicandela (mcd) for 10−3 candela.

# References

{{Authority control SI base units Units of luminous intensity