candela

SI base unit
Name	Symbol	Quantity
candela	cd	luminous intensity
Definition The candela, symbol cd, is the SI base unit of luminous intensity in a given direction. By definition, one candela is equal to one lumen per steradian, where the lumen 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. The unit lm W^‑1 is equal to cd sr W⁻¹, or kg⁻¹ m⁻² s³ cd sr, where the kilogram, metre and second are defined in terms of h, c and Δν_Cs.

One candela is equal to one lumen per steradian.

$1 \ \text{cd} = 1 \ \dfrac{\text{lm}}{\text{sr}}$

The definition of the candela implies the exact relation K_cd = 683 kg^–1 m^–2 s³ cd sr for monochromatic radiation of frequency ν = 540 × 10¹² Hz.

Inverting this relation gives an exact expression for the candela in terms of the defining constants h, Δν_Cs and K_cd :

$1 \mspace{4mu} \text{cd} \mspace{10mu} = \dfrac {K_{cd}}{683} \mspace{6mu} \text{kg} \mspace{6mu} \text{m}{^2} \mspace{6mu} \text{s}{^{-3}} \mspace{6mu} \text{sr}{^{-1}}\\ \\ \\ 1 \mspace{4mu} \text{cd} \mspace{10mu} = \dfrac {1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2 (683)} \mspace{6mu} h \mspace{6mu} {\Delta \nu _{Cs}}^2 \mspace{6mu} K_{cd}\\ \\ \\ 1 \mspace{4mu} \text{cd} \mspace{10mu} = 2.614 \mspace{4mu} 830 \mspace{4mu} 482 \mspace{4mu} 285 \mspace{4mu} 615 \mspace{4mu} 686 \text{...} \times 10^{10} \mspace{6mu} h \mspace{6mu} {\Delta \nu _{Cs}}^2 \mspace{6mu} K_{cd}$

The effect of this definition is that one 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 W sr^-1.

Luminous efficacy

Luminous efficacy is a measure of the brightness of a light source, as perceived by the human eye, relative to the light source’s radiant power. In effect it is the ratio of the luminous flux to radiant intensity.

Luminous intensity

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 standardised model of the sensitivity of the human eye across the visible range of the electromagnetic spectrum.

The definition does not specify the luminosity function for weighting radiation at other frequencies.

The frequency of electromagnetic radiation chosen for the definition of the candela is in the green region of the visible spectrum. The human eye, when adapted for bright conditions, is most sensitive near this frequency. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, according to the frequency response of the human eye.

Radiometry analogy

Luminous intensity is analogous to radiant intensity. However, when calculating radiant intensity, the contributions of each frequency of electromagnetic radiation are treated equally, but for luminous intensity, the contributions of each frequency of light are weighted according to the standard luminosity function.

Essentially, luminous intensity is a measure of the visible component of a radiant intensity.

Luminous intensity and luminous flux

Luminous intensity should not be confused with luminous flux, which is the total perceived power emitted in all directions. Luminous intensity is the perceived power per unit solid angle.

If a lamp has a 1 lumen bulb and the optics of the lamp are set up to focus the light evenly into a 1 steradian beam, then the beam would have a luminous intensity of 1 candela. If the optics were changed to concentrate the beam into 0.5 steradians then the source would have a luminous intensity of 2 candelas. The resulting beam is narrower and brighter, though its luminous flux remains unchanged.

Photometry units

Name	Symbol	Quantity	Expressed in terms of SI base units	Expressed in terms of other SI units
candela	cd	luminous intensity	cd	lm/sr
lumen	lm	luminous flux	cd	cd sr
lux	lx	illuminance	m^-2 cd	lm/m²
candela per square metre	m^-2 cd	luminance	m^-2 cd	cd/m²
lumen second	lm s	luminous energy	s cd	lm s
lumen per watt	lm W^‑1	luminous efficacy	kg^‑1 m^‑2 s³ cd	lm/W