How the capacity is calculated
A belt conveyor moves a continuous ribbon of material. Its capacity is the area of that ribbon's cross-section multiplied by the belt speed. Everything else in the calculation is about finding the cross-section correctly.
On a three-roll troughed belt, the cross-section has two parts. The lower part sits in the trough formed by the centre roll and the two inclined wing rolls. The upper part is the heap above the belt edges, whose slope is set by the surcharge angle. This calculator uses the method of DIN 22101, the German standard for belt conveyors for bulk materials:
b = 0.9 B − 0.05 m
A1 = [l3 + (b − l3) cos λ]² · tan β ÷ 6
A2 = [l3 + (b − l3) ÷ 2 · cos λ] · [(b − l3) ÷ 2 · sin λ]
QV = 3,600 · (A1 + A2) · φ · v
Qm = QV · ρ
- B
- belt width
- b
- usable width: the outer edges of the belt stay free so material does not spill
- l3
- length of the centre idler roll, taken from the standard roll series for each belt width
- λ
- trough angle of the wing rolls
- β
- surcharge angle of the material on the moving belt
- φ
- reduction factor for an inclined conveyor, 1 on a level belt
- v
- belt speed in m/s
- ρ
- bulk density in t/m³
Worked example
An 800 mm belt with 30° troughing carries dry sand (1.6 t/m³, surcharge angle 20°) at 1.6 m/s on the level. The usable width is 0.67 m and the centre roll is 315 mm long. That gives an upper area of 0.0235 m² and a lower area of 0.0416 m², so 0.0651 m² in total. At 1.6 m/s the belt moves 375 m³/h, which is about 600 t/h of sand.
What changes the result most
Belt width has the strongest effect. Capacity grows roughly with the square of the width, so going from 800 mm to 1,000 mm adds about 60 % at the same speed.
Trough angle matters a lot at first. Moving from a flat belt to 20° roughly doubles the cross-section. Beyond 35° the gain is smaller, and steep troughs need belts that can take the bending at the transitions.
Surcharge angle depends on the material. Free-flowing grain or dry cement runs flat, around 10°. Lumpy or sticky material such as wood chips or wet ore holds a steeper heap. If you only know the angle of repose, subtract 10° to 15° as a starting value.
Incline reduces capacity because the heap above the belt edges flattens. At small angles the loss is a few percent. Close to the surcharge angle only the trough part is left, and the material starts to roll back.
Typical values to start from
| Material | Bulk density (t/m³) | Surcharge angle |
|---|---|---|
| Sand, dry | 1.4 – 1.7 | 15° – 20° |
| Gravel | 1.5 – 1.9 | 15° |
| Limestone, crushed | 1.4 – 1.6 | 20° |
| Coal, bituminous | 0.75 – 0.95 | 20° – 25° |
| Iron ore | 2.1 – 2.9 | 20° – 25° |
| Cement, loose | 1.1 – 1.4 | 10° |
| Wheat | 0.72 – 0.82 | 10° |
| Wood chips | 0.2 – 0.4 | 20° – 25° |
Bulk density varies with moisture, grain size and how well the material is compacted. Measure it for your own material when the result matters.
Limits of this calculation
The result is the theoretical capacity for an evenly fed belt with standard idler geometry. Real conveyors rarely run at 100 % fill: feeders surge, material sticks, and transfer chutes limit throughput. A loading of 70 to 80 % is a common planning value. For a final design you also need the drive power and belt tension, which depend on length, lift and friction. Those come from a full calculation to DIN 22101 or CEMA, usually done by the conveyor supplier.