## UNIT: candela

• PID: si:unit:candela
• Definition: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It 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.
• Source: SI Brochure 9th Ed. 2019, p 135
• Reference: CGPM Resolution 1 of the 26th CGPM (2018) "On the revision of the International System of Units (SI)"
• Status: Valid
• Valid: 2019-05-20 -
• Notes
1. This definition implies the exact relation $$K_{\rm{cd}} = 683\ {\rm{cd\:sr\:kg^{-1}\: m^{-2}\:s^{3}}}$$ for monochromatic radiation of frequency $$\nu = 540 \times 10^{12}\ {\rm{Hz}}$$. Inverting this relation gives an exact expression for the candela in terms of the defining constants $$K_{\rm{cd}}$$, $$h$$ and $$\Delta\nu_{\rm{Cs}}$$: $$1\ {\rm{cd}} = \left( \frac{K_{\rm{cd}}}{683} \right)\ {\rm{kg\:m^{2}\:s^{-3}\:sr^{-1}}}$$ which is equal to $$1\ {\rm{cd}} = \frac{1}{(6.626\,070\,15 \times 10^{-34})(9\,192\,631\,770)^{2}\,683} (\Delta\nu_{\rm{Cs}})^{2}\,h\:K_{\rm{cd}}$$ $$\approx 2.614\,830 \times 10^{10} (\Delta\nu_{\rm{Cs}})^{2}\:h\:K_{\rm{cd}}$$
2. 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 $$540 \times 10^{12}\ {\rm{Hz}}$$ and has a radiant intensity in that direction of $$(1/683)\ {\rm{W/sr}}.$$ The definition of the steradian is given below Table 4.
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