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3
V I S I O N   F L O O D
A r c h i t e c t u r a l   F l o o d   L u m i n a i r e
- Inverse Square Cosine Law
F L O O D L I G H T I N G   F U N D A M E N T A L S
E D2
COS (x)
X=45
°
45
°
I=7
07
 cd
D=
10
'
5 fc (10')2
COS (45
°)
=
707 candela
E=fc
I=
E D2
COS (x)
X=30
°
30
°
I=577 cd
5 fc (10')2
COS (30
°)
D=
10
'
=
577 candela
E=5 fc
I=
E D2
COS (x)
X=30
°
30
°
I=2,3
10
 cd
5 fc (20')2
COS (30
°)
D=
20
'
=
2,310 candela
E=5 fc
I=
E D2
COS (x)
X=30
°
I=57
7 cd
5 fc (10')2
COS (30
°)
D=
10
'
=
577 candela
E=5 fc
I=
30
°
Footcandle levels are ultimately dependent upon the projected distance, aiming angle, and luminous  intensity of a lamp/reflector combination. 
A cursory understanding of the equation which relates these variables provides insights to proper design technique and distribution selection.
Holding other variables constant, as the projected distance increases from the luminaire to the surface being illuminated, a greater amount 
of luminous intensity (I, Candela) is required to sustain an equal illuminance (E, Footcandle) level.
I N V E R S E   S Q U A R E   C O S I N E   L A W
E=I cos (x)/D
-or-
Illuminance (Footcandles, fc) = Luminous Intensity (Candelas, Cd) * cos (incident angle X) / Distance
2
Holding incident angle X constant at 30˚ while increasing the projected distance D from 10' to 20' requires an increase in candela from 
577 to 2310 respectively to sustain an equal 5 footcandles (fc) of illumination at the target point.
The incident angle as measured from a luminaire’s directed intensity to the target surface normal also plays a significant role in determining 
illuminance values. Holding other variables constant as the incident angle from the target surface to the projected aiming line increases, so does
the amount of luminous intensity (I, Candela) required to sustain an equal illuminance value.
Holding projected distance D constant at 10' while increasing incident angle X from 30˚ to 45˚ requires an increase in candela from 
577 to 707 respectively to sustain an equal 5 footcandles (fc) of illumination at the target point.
VISION_FLOOD.wpc  11/19/03  6:20 PM  Page 4