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I will venture a guess that LUX can not be converted to PAR. LUX measures the intensity of light, as it would be perceived by the human eye. PAR, is a measure of "Photosynthetic Photon Flux (PPF) for Photo synthetically Active Radiation (PAR) between 400 and 700 nanometers".
In theory, you could have very intense light that is either lower 400 nm and higher than 700, which would not register as a high PAR number. I'm sure these guys know more though
When we are talking about Reef tanks this is realy very confusing for most.
Visable Light is measured in lumn as all the the light emoted between 350nm and 700nm.
PAR is a measurement of the light used for photosynthesis and is in the rang of about 450 nm and 650 nm
Now corals themselves do not use light in all these various wave lenghts they use light primarly in two sepearte band mainly from 417nm to 485 nm as a blue band and from 625nm to 655nm whch is the red band.
In reality you could have lighting source with a lot of light in the 500nm to 600 nm range that would give a very high PAr reading as well as a high LUMs rating but would be nearly useless for coral growth.