The shape, then the two multiplications
A troughed belt divides into three equal rolls once the unloaded edge is taken off each side. At the defaults — a 36 in belt with 1.5 in left clear at each edge — 33 in carries material, so each roll spans 11 in. The two wings tip up at the idler angle and the material heaps above the line joining their tops at the surcharge angle.
At 35 degree idlers the trough itself works out at 126.3 sq in, and a 20 degree heap on the 29 in chord across the top adds another 49.8 sq in. That is 176.1 sq in of load, or 1.223 sq ft. At 350 ft per minute the belt presents 427.9 cubic feet a minute, and at 100 lb per cubic foot that is 42,793 lb a minute, which is 1,283.8 tons an hour.
Nothing in that chain is difficult. What makes conveyor capacity arithmetic go wrong is the units on either side of it, which is why the page prints the intermediate rates rather than jumping to tons.
Feet per minute against feet per second
350 ft per minute is 5.83 ft per second. Both are ordinary numbers for a bulk belt and neither carries its unit when somebody writes it on a drawing or reads it over the phone. Substituting one for the other is a factor of 60, which turns 1,283.8 tons an hour into 21.4 — still a believable conveyor, which is exactly the problem. Tons an hour against pounds a minute is a factor of 33.33 in the other direction and behaves the same way.
The heap is the part you know least about
At the defaults the heap above the trough is 28 percent of the whole section, so a third of the capacity rests on an angle nobody measured. The surcharge angle is not the angle of repose of a static pile — a moving belt over vibrating idlers settles the material flatter, and by how much depends on the material, the moisture in it and the speed. Pouring a cone in the yard gives you the repose angle; what your engineer subtracts from it for a belt in motion is their call, not this page's, and the table on the page exists so you can see what that call costs.
Trough angle has diminishing returns
Going from a flat belt to 20 degree idlers adds a lot of section. Going from 35 to 45 adds much less, because the wings are approaching vertical and the extra area they enclose comes at the price of the horizontal width they no longer project. Whether a given belt will run in a deep trough without distress at the junction between the flat centre and the wings is a belt-construction question for the supplier, and this page has no opinion on it.
Questions people ask
How do I calculate the capacity of a belt conveyor?
Find the cross-sectional area of the load, multiply by belt speed to get a volume rate, and multiply that by bulk density to get a mass rate. The area is the trough the idlers form plus the heap standing above it at the surcharge angle. At 1.223 sq ft of load, 350 ft per minute and 100 lb per cubic foot that is 427.9 cubic feet a minute, 42,793 lb a minute, and 1,283.8 tons an hour.
What is the difference between angle of repose and surcharge angle?
Angle of repose is the slope a static poured pile holds. Surcharge angle is the slope the same material holds on a belt that is moving over idlers, and it is normally the smaller of the two because the belt is being shaken. This page takes the surcharge angle as your input rather than deriving it, because how much your material flattens on a running belt depends on the material and the speed and is something you measure, not something a table can tell you.
Why does my calculated tonnage not match what the belt scale says?
Usually the section is not full. A belt fed by a hopper gate or a feeder rarely carries the theoretical profile all shift, and the surge and starve either side of the average does not cancel out in tonnage the way people expect. Cut the belt over a measured length while it is stopped and isolated, weigh what came off, and you have your own pounds per foot to compare against the calculated one.
Does a wider belt or a faster belt give more capacity?
Both, but not on the same terms. Capacity is linear in speed and roughly quadratic in usable width, since width sets both the trough dimensions and the chord the heap sits on. Which one you can actually change is set by the frame you own and by what the material does when it lands on a faster belt, and neither of those limits appears anywhere in the arithmetic.
What belt speed should I run?
This page will not say. Belt speed is limited by what the material does at the loading point and the discharge, by belt and idler life, by carryback and dust, and by what the drive and the structure were designed around. All of those come from the conveyor maker and from the engineer responsible for the installation. What the page will do is tell you what any speed you enter is worth in tons an hour.