Lumens & Foot-Candles

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Willarch

July 17, 2025 21:11

Foot-candles are calculated as lumens per square foot.  So if I have a 1,000 lumen light source and a 10 sf surface, the foot-candles (the illumination of that surface) are therefor 100.  Fine.  If I move that 10 sf surface twice as far from the light source, intuitively the illumination on the surface will be less.  Mathematically, I think it would be 1/4 as much (the reciprocal of twice the distance squared).  But if I again plug the 1,000 lumens and 10 sf into the formula for foot-candles, I still get 100 foot-candles, and not 25.  What am I missing??

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  JCorrington July 17, 2025 22:40

  I never got a lighting question on my exams. At least not one that needed math. To answer your question, I have no idea because I didn't study lighting calculations :P

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  Galchenko12 July 18, 2025 00:05

  Footcandles (fc) = Intensity (candelas) / Distance² (ft²). Foot candles are inversely proportional to the distance.

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  Willarch July 18, 2025 05:05

  The formula in the ARE 5.0 Guidelines is:

  Foot-candles = lumens ÷ area in ft^2

  Presumably "area in ft^2" is the area expressed as square feet.

  If the light source is 1,000 lumens, that value is fixed.

  If the surface area is 10 square feet, that value is also fixed.

  So according to the formula, there are 100 foot-candles, period.  I don't see how the formula accommodates distance...  

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  lyfian0924 September 05, 2025 19:40 (Edited September 05, 2025 19:40)

  You have to multiple the Coefficient of Utilization to the Lumen. And the Coefficient of Utilizations can be found through a table based on the Room Cavity, material reflectance... The Room Cavity is an equation of 2.5x(wall Area)/(work Plan Area), so here you can see the distance been considered. Again, this is for the work plan right below the lighting source. If you want to calculation something with an angle to the lighting, sin or cos needs to be multiplied to calculation either the vertical or horizontal illuminance (lux).

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