Horsepower is a measure of work that a machine performs and loosely speaking is, Force (in lbs) multiplied by Speed (in feet per minute) divided by 33000. (Assuming this is a horizontal steel belt conveyor)
So, first you must add up all the weight of every component being driven, drive shaft(s), driven shaft, drums belt will ride on, sprockets, chain, couplings, mesh belt and of course the weight of the part(s) on the mesh belt.
Each belt will have a co-efficient of friction that the belt manufacturer can give you.
Total Weight x co-efficient of friction x belt speed (in feet/min.) = foot lb. of work
x 1.25 for inefficiencies of assemblies (e.g. sprocket mis-alignment, low on lube etc.)
x 1.25 for 'over-load' factor
now, divide this ft.lbs/min answer, by 33,000 to get horse power
It will never be a 'whole' number, so round it up to the next easiest hp rating. It is better to err on the safe side and account for unforeseen abuse by operators.
Should the application be other than horizontal, say inclined, then additional factoring may be needed.
Let us know if this answers you question, or, give us the needed numbers as indicated above and we can verify!
Good Luck!
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"A problem well stated is a problem half solved." Charles F. Kettering