The candela (symbol: cd) is the unit of
luminous intensity
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 huma ...
in the
International System of Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
(SI).
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
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats.
In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
of light in the source's spectrum, the contribution of each wavelength is
weighted by the
luminous efficiency function, the model of the sensitivity of the human eye to different wavelengths, standardized by the CIE and
ISO
The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries.
Me ...
.
A common wax
candle
A candle is an ignitable candle wick, wick embedded in wax, or another flammable solid substance such as tallow, that provides light, and in some cases, a Aroma compound, fragrance. A candle can also provide heat or a method of keeping time. ...
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
Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...
for ''candle''. The old name "candle" is still sometimes used, as in ''
foot-candle'' 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 , ''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 spectral band, band of the electromagnetic spectrum that is visual perception, visible to the human eye. Electromagnetic radiation in this range of wavelengths is called ''visible light'' (or simply light).
The optica ...
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 com ...
, corresponding to a wavelength of about 555 nanometres. The
human eye
The human eye is a sensory organ in the visual system that reacts to light, visible light allowing eyesight. Other functions include maintaining the circadian rhythm, and Balance (ability), keeping balance.
The eye can be considered as a living ...
, when
adapted for bright conditions, is most sensitive near this frequency. Under these conditions,
photopic vision
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 vis ...
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 is the
luminous intensity
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 huma ...
, is the
radiant intensity and
is the
photopic luminous efficiency function. If more than one wavelength is present (as is usually the case), one must integrate over the
spectrum
A spectrum (: spectra or spectrums) is a set of related ideas, objects, or properties whose features overlap such that they blend to form a continuum. The word ''spectrum'' was first used scientifically in optics to describe the rainbow of co ...
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. A solid angle in the fo ...
s), it will have an intensity of
* Focused into a 20° beam (0.095 steradians), the same light bulb would have an intensity of around 18,000 cd or 18 kcd 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 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 le ...
per hour. Germany, Austria and Scandinavia used the
Hefnerkerze, a unit based on the output of a
Hefner lamp.
A better standard for luminous intensity was needed. In 1884,
Jules Violle had proposed a standard based on the light emitted by 1 cm
2 of
platinum
Platinum is a chemical element; it has Symbol (chemistry), symbol Pt and atomic number 78. It is a density, dense, malleable, ductility, ductile, highly unreactive, precious metal, precious, silverish-white transition metal. Its name origina ...
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
Redox ( , , reduction–oxidation or oxidation–reduction) is a type of chemical reaction in which the oxidation states of the reactants change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is ...
, and could be obtained in pure form.
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.
[ 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
Black-body radiation is the thermal radiation, thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific ...
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.
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 measurement, measuring electromagnetic radiation, including visible light. Radiometric techniques in optics characterize the distribution of the radiation's power (physics), power in space, as opposed to phot ...
, 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 that direction of watt
The watt (symbol: W) is the unit of Power (physics), 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 quantification (science), quantify the rate of Work ...
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. A solid angle in the fo ...
.
The definition describes how to produce a light source that (by definition) emits one candela, but does not specify the luminous efficiency 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 luminous efficiency function. An appendix to the SI Brochure makes it clear that the luminous efficiency 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 a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of U ...
(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 revision of the SI
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 artefacts such as the standard kilogram.
Effective 20 May 2019, the 144th ...
, 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 (in candelas) in a well-defined cone, the total luminous flux in lumens is given by