The TPH equation is TPH = belt speed (ft/min) × cross-sectional load area (ft²) × bulk density (lb/ft³) × 60 min/hr ÷ 2000 lb/ton [S3]. The metric form is TPH = 3.6 × belt speed (m/s) × load cross-section (m²) × material density (t/m³) [S1]. Belt width sets the maximum possible cross-section, not the rated TPH by itself [S1].
In practice, a 24-inch belt handles light loads or short runs, 36–42-inch belts are common on secondary lines, 48–60-inch belts run most primary mine conveyors, and 72-inch-and-up belts appear on high-tonnage coal, salt, and aggregate runs [S1]. Two conveyors with identical belt width can still show very different TPH if speed, troughing angle, or material density change [S1].
The TPH formula and unit conversion
The core relation is Q = A × v × ρ, where A is cross-sectional area, v is belt speed, and ρ is bulk density [S5]. Converted to the imperial TPH form, it becomes TPH = v (ft/min) × A (ft²) × ρ (lb/ft³) × 60 ÷ 2000 [S3][S7]. Mixing units (e.g. ft/min with kg/m³) requires explicit conversion before substitution [S3].
For metric work, TPH = 3.6 × v (m/s) × A (m²) × ρ (t/m³); the 3.6 constant folds in 3600 s/h ÷ 1000 kg/t [S1]. A separate shortcut, bulk capacity Q (TPH) = A (ft²) × v (ft/min) × ρ (lb/ft³) ÷ 33.333, is also used in vendor calculators [S7]. The 1/2000 and 1/33.333 forms agree numerically because 2000 lb/ton × 60 min/h = 120,000, and 33.333 × 120,000 / 60 collapses the same factor.
Working example: 300 ft/min, 0.5 ft², 100 lb/ft³
Plug the numbers in directly: TPH = 300 × 0.5 × 100 × 60 ÷ 2000 = 450 TPH [S3]. This is the worked example published in miningdoc.tech's step-by-step guide, using a 36-inch-class troughed belt carrying an average 100 lb/ft³ bulk solid such as crushed limestone or coal [S3][S4]. The 0.5 ft² load area is consistent with CEMA-style troughed geometry on a 36-inch belt at 35° idler angle with a typical surcharge [S4].
To cross-check with the Q = A × v × ρ form, 0.5 ft² × 300 ft/min = 150 ft³/min, times 100 lb/ft³ = 15,000 lb/min, times 60 = 900,000 lb/h, divided by 2000 = 450 TPH [S3][S5]. If a feeder limits the actual load height to less than the geometric full trough, recompute A from the measured height; the formula will punish any over-claim by overstating TPH [S3].
How belt width controls the cross-sectional area
Belt width alone does not appear in the TPH formula, but it caps the maximum load cross-section, and the belt conveyor cross-section is what feeds the equation [S1][S4]. A 36-inch (900 mm) troughed belt at 35° idler angle typically carries around 0.5 ft² of load at design surcharge; the exact figure comes from CEMA-style tables for each belt width and troughing combination [S4].
Standard troughing angles for mining belts are 20°, 35°, and 45°, with 35° as the most common compromise between capacity and belt training [S3]. Going from 20° to 35° enlarges the cross-section and therefore the TPH for the same belt width and speed, while 45° is reserved for very free-flowing material because it stresses the belt carcass and idler seals [S1][S3]. Flat belts, used for short or light-duty runs, carry noticeably less cross-section at any given width and so deliver lower TPH [S1].
Selecting belt speed, surcharge angle, and density
Belt speed is a design choice, not a free variable. Higher speed raises TPH linearly but also raises spillage, idler wear, and noise, and over-speeding can cause mistracking and accelerated pulley wear [S1][S2]. For most bulk-solids applications, belt speed sits between 300 and 600 ft/min; mining long-distance and high-tonnage lines often run 800–1,200 ft/min on wide steel-cord belts where the carcass can take the tension [S1].
Surcharge angle is normally 5°–15° less than the material's angle of repose, which controls the top contour of the load on the belt and therefore A [S3]. Bulk density ρ is material-specific: crushed stone runs near 90–110 lb/ft³, bituminous coal near 50–60 lb/ft³, and damp sand or iron ore fines can hit 120–150 lb/ft³, which means the same belt geometry yields 2–3× the TPH on heavy ore versus light coal [S3]. For inclined runs, effective cross-section drops with slope, and a separate downhill correction is needed for decline conveyors carrying recoverable material [S3].
Comparison of common belt types at the same width
At a fixed width, the practical capacity ranking from lowest to highest is: flat belt → pipe belt → troughed belt → steel-cord troughed belt [S1]. Pipe conveyors win on dust and spillage control but lose 15–25% of the cross-section compared with an open trough of the same width because the belt edges roll inward [S1]. Steel-cord belts do not increase cross-section directly, but they allow higher allowable tension and higher belt speed, which compounds into higher TPH on long, high-tonnage runs [S1].
On a 48-inch belt, troughed steel-cord at 35° running 600 ft/min can deliver several thousand TPH on dense ore; a flat fabric belt at the same 48-inch width and 300 ft/min will deliver a small fraction of that, mainly because of cross-section rather than width [S1][S4]. When evaluating a mesh belt conveyor for light-duty or food applications, the same Q = A × v × ρ logic applies, but belt width is usually much smaller and belt speed is limited by the mesh weave and product stability.
Common mistakes that make the TPH calculation wrong
The three most common errors are unit mixing, double-counting the time constant, and trusting nominal belt width instead of measured load height [S3][S5]. Unit mixing is by far the most damaging: if v is in m/s, A in ft², and ρ in lb/ft³, the answer is off by a factor of 19.5 and the motor or downstream chute will be sized wrong [S3]. A second class of error treats the constant 3.6 as universal; it only applies when v is in m/s, A in m², and ρ in t/m³; using it with any other unit set silently gives a wrong TPH [S1][S3].
Overloaded belts show up as spillage, inconsistent loading, and accelerated idler wear; underloaded belts waste capex on a frame, drive, and belt that the duty never justifies [S1][S2]. For variable-speed drives that adjust v on the fly, the TPH equation is still valid per instant, but plant throughput depends on the average v over a shift, so integrating logged v gives a more honest shift TPH than a single setpoint. Where downstream equipment is sensitive, sizing the drive with a variable speed drive sized for 110–120% of calculated TPH gives margin without paying for a fully oversized motor.
Standards, references, and trackable signals
The CEMA Belt Conveyors for Bulk Materials publication is the de-facto reference for cross-section, idler spacing, and pulley diameters used in these calculations, and is cited by the 2026 PDHonline M344 practical-calculations course as the underlying methodology [S4]. ISO 5048 / ISO 5049 and DIN 22101 are the parallel European references for conveyor design and idler selection, and they agree on the Q = A × v × ρ form though they differ in the surcharge-angle table values [S4]. For audit traceability, the most defensible approach is to state which standard governed each input (width → CEMA, surcharge angle → CEMA or ISO 5048, density → material handbook or lab test).
Trackable signals for the next design review: (1) the mine or plant's measured bulk density on the actual as-handled material, not the textbook value; (2) the measured load height on the belt at design feed rate, not the theoretical full-trough area; and (3) the logged belt speed from the drive VFD rather than the nameplate, since v actually drops under load on many long conveyors [S3][S5]. For related sizing work, the gearbox behind the drive pulley is selected on torque × speed, and the method for that is covered in a sibling piece on sizing a gearbox for a belt conveyor drive; for drive-side electrics, a phased vs single-shutdown PLC migration plan should be aligned with any new VFD roll-out.