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Lighting Terminology and Definitions

The unit of luminous intensity I is the candela (cd) also known as the international candle. The intensity of a light source is commonly referred to as its candlepower.

The unit of luminous flux F is the lumen (lm).  One lumen is equal to the luminous flux which falls on each square meter (m2) of a sphere one meter (1m) in radius when a 1-candela isotropic light source (one that radiates equally in all directions) is at the center of the sphere.  Since the area of a sphere of radius r is 4πr2, a sphere whose radius is 1m has 4πm2 of area, and the total luminous flux emitted by a 1-cd source is therefore 4π1m.

Thus the luminous flux emitted by an isotropic light source of intensity I is given by:

F  =  4πI  where

Luminous flux (lm)  =  4π × luminous intensity (cd)


The illumination (or illuminance) E of a surface is the luminous flux per unit area that reaches the surface:

E  =  F/A Illumination   =   luminous flux / area

Luminous Intensity & Luminous Flux

lumens = 4π × cd                             cd = lumens

lumens  =  4π  ×  (Mean Spherical Candlepower) 

fc = cd                                           cd = fc × d2

lumens = fc  4π× d2                      fc = lumens
                                                            4π× d2


Inverse Square Law:   E =   I

Cosine Law:                             E =  I cosq
wheree q is angle of incidence                d2                

Related Formulas
10.764 × fc = lux     
1 lux = 0.0929 fc

10.764 × lumens / sq. ft = lux 

lumens / m² = lux

1 cd / sq. ft. = π × fL  (foot-Lambert)

3.426 × fL = nits = cd / m²

1 fL = 1 lumen / sq. ft. 

1 fL = 3.426 cd / m²  

1 cd = 1 lumen per steradian (unit solid angle), where “steradianunit solid angle is a cone.  Unit solid angle is photometric brightness, where the spherical surface is:  
S = 4π²  

If  r = 1, then there are 4π lumens in the sphere, (12.566 lumens)