# Re: watts vs. lumens

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Regarding the discussion about lumens/Watts/PAR/etc. you techies on
the list can look at

http://www.cs.indiana.edu/hyplan/kuzimmer/IES/section3.2.html

Lumens are units of luminous flux, and this quantity is defined based
on an integral over wavelength or frequency. Thus the assertion that
"For any given freqency lumens can can be converted to either watts or
PAR values" is meaningless. Lumens cannot be computed in any given
infinitesimal frequency/wavelength interval, but only in a finite range
of frequency/wavelength. Thus a spectral plot can never have lumens
in the vertical axis.

To translate the relative units used by lamp manufacturers into Watts
one first have to compute the integral under the spectral curve. One
could copy the curve onto graph paper and estimate the area by counting
squares. This total area S (in units such as inches X nanometers)
corresponds to the lamp output in Watts P thus one just have to multiply
the vertical axis by P/S to get the lamp spectrum in Watts/nm. Of course,
this assumes 100% conversion efficiency. Following the same principles one
could also multiply this spectrum by the photopic curve (e.g. in
http://www.reefnet.on.ca/gearbag/wwwlux.html)
and compute the integral to get the lamp output in lumens. Comparison
of this figure with the manufacturer's published lumen rating for the
lamp should give an idea of the conversion efficiency.

The same procedure could be used with a photosynthesis action spectrum
in place of the photopic curve. This would give the lamp output in