SI REFERENCE POINT
Version: 1.0 Beta , last update: 2024-09-23

candela

The candela, symbol $\rm{cd}$, 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 ${540 \times 10^{12}}\ {{\rm{Hz}}}$, ${K_{\rm{cd}}}$, to be ${683}$ when expressed in the unit ${\rm{lm}}\ {\rm{W}}^{-1} $, which is equal to ${\rm{cd}}\ {\rm{sr}}\ {\rm{W}}^{-1}$, or ${\rm{cd}}\ {\rm{sr}}\ {\rm{kg}}^{-1}\ {\rm{m}}^{-2}\ {\rm{s}}^{3}$, where the kilogram, metre and second are defined in terms of ${h}$, $c$ and $\Delta\nu_{\rm{Cs}}$.

This definition is valid from 2019-05-20
Unit candela
Symbol cd
Quantity luminous intensity
Defining Constant luminous efficacy
Defining Resolution
CGPM Resolution 1 (2018)
Unit Type SI base unit
Defining Equation $$1\;{\rm{cd}} = \left(\frac{{K_{\rm{cd}}}}{683}\right) {\rm{kg}}\;{\rm{m}}^2\;{\rm{s}}^{-3}\;{\rm{sr}}^{-1}$$
Notes:
  1. This definition implies the exact relation ${{K_{\rm{cd}}}} = {{683}}\ {{\rm{cd}}\:{\rm{sr}}\:{\rm{kg}}^{-1}\:{\rm{m}}^{-2}\:{\rm{s}}^{3}}$ 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 $\Delta\nu_{\rm{Cs}}$: $$1\;{\rm{cd}} = \left(\frac{{K_{\rm{cd}}}}{{683}}\right)\ {\rm{kg}}\ {\rm{m}}^2\ {\rm{s}}^{-3}\ {\rm{sr}}^{-1}$$ which is equal to $$1\;{\rm{cd}} = \frac{1}{(6.626\:070\:15 \times 10^{-34})\:({9\:192\:631\:770})^{2}\:{683}} (\Delta\nu_{\rm{Cs}})^{2}\:{h}\:{K_{\rm{cd}}} \approx 2.614\:8305 \times 10^{10} (\Delta\nu_{\rm{Cs}})^{2}\:{h}\:{K_{\rm{cd}}}$$.
  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 ${1/{{683}}}\ {\rm{W}\ \rm{sr}^{-1}}$ The definition of the steradian is given below Table 4.