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Conveyor Belt Calculator — Capacity, Drive Power & Belt Tensions (ISO 5048)

Governing standard: ISO 5048· ISO 5048:1989 (bulk material capacity & drive power) · DIN 22101 troughed-idler cross-section geometry · CEMA 7th ed. tension profile

How ISO 5048 works — the method explained

The MechanixCalc conveyor belt calculator sizes and verifies troughed belt conveyors to ISO 5048 — the international standard for the calculation of operating power and tensile forces in belt conveyors with carrying idlers. Enter the belt width, speed, trough angle, material, conveyor length and lift height, and the tool returns the mass capacity (t/h), volumetric capacity (m³/h), main and secondary resistances, drive shaft power, belt tensions and take-up travel in one pass.

It is built for bulk-materials handling, mining and process-plant engineers who need a defensible, standard-cited calculation for a new conveyor or a capacity audit on an existing installation — together with a full PDF report they can hand to a reviewer. The tension-profile tab applies the CEMA method to map tight-side and slack-side tensions along the belt circuit; the trajectory tab models material discharge off the head pulley; and the startup tab sizes motor starting requirements.

What this calculator does

  • ISO 5048 bulk material capacity in t/h and m³/h for three-roll troughed idler geometry (DIN 22101 equal-roll cross-section)
  • Drive power and motor selection: main resistance F_H, secondary resistance F_N (with the ISO 5048 length factor C), incline/decline lift resistance F_St
  • Belt tensions (tight side T₁, slack side T₂) using Euler's belt-friction formula, minimum sag tension and belt-strength utilisation
  • Idler load per roll, carry-run belt sag percentage and the DIN 22101/CEMA 1.5 % sag limit check
  • Take-up travel and recommended take-up range from belt elongation (ISO 9856 per-unit-width modulus)
  • Discharge trajectory off the head pulley — departure angle, landing distance and maximum height
  • Branded PDF engineering report with full method, input table and results

Method & formulas

Capacity and cross-section area (ISO 5048 / DIN 22101)

The volumetric capacity of a troughed belt conveyor is the product of the load cross-section area A (m²) and the belt speed v (m/s), scaled to t/h by the material bulk density. The cross-section is the sum of the trough trapezoid A₂ (below the chord between wing-roll tips) and the surcharge cap A₁ (the triangular pile above the chord at the dynamic surcharge angle φ). The usable belt width b = 0.9B − 0.05 m allows for edge spillage; the three equal-length rolls each contact b/3 of that width.

Mass capacity then follows directly from the volumetric rate, and the material belt-load per metre q_G (kg/m) is used in all resistance calculations downstream.

Volumetric and mass capacity
Q_v = 3600 · A · v [m³/h]; Q_m = Q_v · ρ / 1000 [t/h]

where A = load cross-section area (m²); v = belt speed (m/s); ρ = bulk density (kg/m³)

Cross-section area (3-roll equal-length troughed idler)
A = A₁ + A₂; A₁ = 0.25 · tan φ · b₁²; A₂ = (l + w · cos λ) · w · sin λ

where λ = trough angle; φ = dynamic surcharge angle; b = 0.9B − 0.05 m (usable width); l = b/3 (centre-roll contact); w = (b − l)/2 (wing-roll contact); b₁ = l + (b − l)·cos λ (top chord)

Drive power (ISO 5048 resistance method)

ISO 5048 splits the total effective pull F_U into the primary (main) resistance F_H — arising from idler rolling friction, belt bending and material flexure over the full length L — and a secondary resistance F_N that accounts for loading-chute forces, pulley bearing friction and belt-cleaning devices on short to medium belts. The ratio C = (F_H + F_N) / F_H is the length factor tabulated in ISO 5048 Table 2; it approaches 1.0 for very long belts and rises to ~3.6 for conveyors shorter than 20 m. The incline lift resistance F_St is material-only (the belt's weight on the carry run is offset by its weight on the return run in the closed loop). Shaft power and motor input power follow directly.

Main resistance and total effective pull
F_H = f · L · g · (q_RO + q_RU + (2·q_Belt + q_G)·cos δ); F_U = C · F_H + F_St

where f = artificial friction coefficient (ISO 5048, typically 0.016–0.030); L = conveyor length (m); g = 9.81 m/s²; q_RO, q_RU = rotating idler mass per metre on carry and return runs (kg/m); q_Belt = belt mass per metre (kg/m); q_G = material load per metre (kg/m); δ = incline angle; C = length factor (ISO 5048 Table 2); F_St = q_G · H · g (N)

Motor input power
P_M = F_U · v [W]; P_motor = P_M / (1000 · η) [kW]

where v = belt speed (m/s); η = drive-train efficiency (gearbox + coupling, typically 0.93–0.97)

Belt tensions, sag and take-up (Euler / DIN 22101 / ISO 9856)

The tight-side tension T₁ and slack-side tension T₂ are related by the Euler belt-friction equation for the drive pulley wrap angle α and the rubber-to-steel friction coefficient μ. The minimum slack-side tension is set by the sag limit: the DIN 22101 / CEMA criterion requires that the carry-run belt sag ratio (droop/span) stays below 1.5 % to prevent material spillage and excessive idler impact loading. The calculator checks the sag at the slack side — the lowest tension point on a head-driven conveyor — where under-tension is most likely. Take-up travel is derived from the belt elongation at average tension using the ISO 9856 per-unit-width elastic modulus; the recommended take-up range adds a 50 % installation and wear allowance.

Euler belt-friction (drive pulley)
T₁ / T₂ = e^(μ · α); T₁ = F_U · e^(μα) / (e^(μα) − 1); T₂ = T₁ − F_U

where μ = rubber-to-steel friction coefficient (≈ 0.35 for clean dry conditions); α = wrap angle (rad); F_U = total effective pull (N)

Carry-run sag ratio and minimum tension
sag% = (w · S_i) / (8 · T₂) × 100; T_min = w · S_i / (8 · 0.015)

where w = (q_G + q_Belt)·g = distributed carry-run load (N/m); S_i = carry idler spacing (m); T₂ = slack-side belt tension (N); 0.015 = 1.5 % sag limit

Worked example

Estimate the shaft drive power and select a motor for a flat troughed belt conveyor carrying coal (bulk density 800 kg/m³) at 450 t/h. Belt width 1000 mm, belt speed 2.0 m/s, conveyor length 200 m (flat, H = 0). Drive efficiency η = 0.95. Use the ISO 5048 main-resistance only (C ≈ 1.45 for L = 200 m, f = 0.020). Belt mass q_Belt = 6.5 kg/m; neglect idler rotating mass for this estimate.

Given

  • Mass capacity Q_m450 t/h
  • Belt speed v2.0 m/s
  • Conveyor length L200 m
  • Lift height H0 m (flat)
  • ISO 5048 friction coefficient f0.020
  • Length factor C (ISO 5048 Table 2, L = 200 m)1.45
  • Belt mass q_Belt6.5 kg/m
  • Drive efficiency η0.95

Result

  • Material load q_G62.5 kg/m
  • Main resistance F_H2 963 N
  • Total effective pull F_U (with C = 1.45)4 296 N
  • Shaft power P_M8.6 kW
  • Motor input power required9.0 kW
  • Selected standard motor11 kW
  1. Convert mass capacity to material load per metre: q_G = Q_m × 1000 / (3600 × v) = 450 × 1000 / (3600 × 2.0) = 450 000 / 7200 = 62.5 kg/m.
  2. On a flat conveyor (cos δ = 1, F_St = 0) the main resistance is F_H = f · L · g · (2·q_Belt + q_G) = 0.020 × 200 × 9.81 × (2×6.5 + 62.5) = 0.020 × 200 × 9.81 × 75.5.
  3. F_H = 0.020 × 200 × 9.81 × 75.5 = 3 924 × 0.020 × 75.5... compute step by step: 200 × 9.81 = 1962; 1962 × 75.5 = 148 131; 148 131 × 0.020 = 2 962.6 N.
  4. Apply the ISO 5048 length factor: F_U = C · F_H = 1.45 × 2962.6 = 4 295.8 N (secondary resistances on a 200 m belt add ~45 % over the main resistance).
  5. Shaft power: P_M = F_U × v = 4 295.8 × 2.0 = 8 591.6 W = 8.59 kW.
  6. Motor input power: P_motor = P_M / η = 8.59 / 0.95 = 9.04 kW. Select the next standard motor size: 11 kW.

Illustrative example — verify against your actual cross-section area (for the capacity check), idler rotating-mass contributions and belt tensions in the full calculator. The 11 kW motor also needs a starting-torque check before selection is finalised.

Frequently asked questions

Which standard does this conveyor belt calculator use?

The primary governing standard is ISO 5048:1989 (Continuous mechanical handling equipment — belt conveyors with carrying idlers — calculation of operating power and tensile forces). The three-roll troughed cross-section area follows the DIN 22101 equal-roll geometry. The tension profile tab uses the CEMA 7th edition minimum-sag tension criterion, and belt elastic elongation uses the ISO 9856 per-unit-width modulus. The governing method and standard clause are reproduced in the generated PDF report.

What is the ISO 5048 length factor C and why does it matter?

C is the secondary-resistance correction factor from ISO 5048 Table 2. It accounts for material-loading, pulley-bearing and belt-cleaning resistances that are independent of conveyor length. Short conveyors (< 50 m) carry a large overhead — C can reach 2.1–3.6 — so neglecting it significantly under-sizes the drive. For long conveyors (> 1000 m) C approaches 1.05 and secondary resistances become a small fraction of the total. The calculator interpolates C from the ISO 5048 table for any conveyor length.

How is belt sag checked and why does it matter?

Belt sag is the ratio of the carry-run belt droop to the idler spacing, expressed as a percentage. DIN 22101 and CEMA require this to stay below 1.5 % to prevent material spillage at the idler junctions and to limit the dynamic impact load on the idler rolls. The calculator evaluates sag at the slack-side tension T₂ — the minimum tension on the carry run of a head-driven conveyor — which is the correct, conservative point to check. If sag exceeds 1.5 % a warning is shown and the minimum required tension is reported.

Can I analyse an inclined or declined conveyor?

Yes. Enter a positive lift height H for an uphill conveyor (the incline adds the material lift resistance F_St = q_G·H·g to the effective pull) and a negative H for a decline. Steep inclines trigger a warning at > 18° — the typical limit for most bulk materials on a standard belt; above that a cleated belt or an alternative conveyor type should be considered. The full incline angle δ = arcsin(H/L) feeds the cosine correction on the running resistance.

Is the conveyor belt calculator free?

You can run a full calculation during a free 30-minute preview with no sign-up required. A free 14-day account trial unlocks every calculator on the platform with no credit card needed. The branded PDF engineering report and the ability to save and reload calculations are part of a paid plan.

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