Conveyor effective tension and belt tension calculator
From conveyor length, lift, speed and capacity to Te, drive power, T1, T2, the sag minimum and the counterweight force — in one chain.
Result
How it works
Most conveyor checks need a tension at a specific point: the motor needs Te, the belt rating needs T1, the take-up needs T3. This calculator chains them together using the simplified length-coefficient method published by Rulmeca: resistances on the carrying and return sides, effective tension, power, the slack-side tension needed to stop the drive slipping, and the minimum tension needed to keep belt sag between idlers within limit.
Whichever of slip or sag needs the higher tension governs. The result gives the maximum tension T1 (send it straight to the belt rating check) and the force the tail counterweight must apply.
Formula
qG = Q / (3.6 v) k = L × Cq × Ct × f Fa = g [k (qb + qG + qRO) + (qG + qb) H] Fr = g [k (qb + qRU) − qb H] Te = Fa + Fr P = Te × v / η Cw = 1 / (e^(μθ) − 1) T2 = Te × Cw T3 = T2 + Fr T0 = g (qb + qG) a0 / (8 × sag) if T3 < T0: T3 = T0, T2 = T3 − Fr T1 = Te + T2 Tail counterweight force = 2 × T3 (g = 9.81, forces in N)
| Symbol | Meaning | Unit |
|---|---|---|
| L | Conveyor length between pulley centres | m |
| H | Lift (+) or drop (−) from tail to head | m |
| v | Belt speed | m/s |
| Q | Capacity | t/h |
| qb | Belt mass per metre | kg/m |
| qG | Material mass per metre | kg/m |
| qRO, qRU | Rotating mass of carrying / return idlers per metre (roll mass ÷ pitch) | kg/m |
| Cq | Length coefficient for secondary resistances (Rulmeca table) | — |
| Ct | Temperature coefficient (1 at +20 °C and above) | — |
| f | Idler rotating friction factor (≈0.016–0.02 normal; 0.023–0.027 difficult) | — |
| η | Drive efficiency | — |
| μ, θ | Drive pulley friction and wrap angle | —, ° |
| a0 | Carrying idler pitch | m |
| sag | Allowed sag between carrying idlers (2 % typical) | % |
| T1, T2, T3 | Tight side, slack side and tail tensions | kN |
Worked example
Inputs: Conveyor length L = 150 m; Lift H (+ up, − down) = 15 m; Belt speed v = 2.3 m/s; Capacity Q = 1000 t/h; Belt mass qb = 9.9 kg/m; Carrying idler rotating mass qRO = 14.8 kg/m; Return idler rotating mass qRU = 4.4 kg/m; Length coefficient Cq = 1.5 —; Temperature coefficient Ct = 1 —; Idler friction factor f = 0.017 —; Drive efficiency η = 0.86 0–1; Drive friction μ (verify) = 0.35 —; Wrap angle θ = 200 °; Carrying idler pitch a0 = 1.2 m; Allowed sag = 2 %; Belt width B = 1000 mm.
- qG = 1000 / (3.6 × 2.3) = 120.8 kg/m; k = 150 × 1.5 × 1 × 0.017 = 3.825
- Fa = 9.81 × [3.825 × (9.9 + 120.8 + 14.8) + (120.8 + 9.9) × 15] = 24.69 kN
- Fr = 9.81 × [3.825 × (9.9 + 4.4) − 9.9 × 15] = -0.92 kN
- Te = Fa + Fr = 23.77 kN; P = Te × 2.3 / 0.86 = 63.6 kW
- Cw = 1/(e^(0.35 × 200 × π/180) − 1) = 0.418; T2 = Te × Cw = 9.93 kN; T3 = T2 + Fr = 9.01 kN
- Sag minimum T0 = 9.81 × (9.9 + 120.8) × 1.2 / (8 × 0.02) = 9.61 kN — larger than T3, so sag governs: T3 = 9.61 kN
- T2 = T3 − Fr = 10.53 kN; T1 = Te + T2 = 34.30 kN (34.3 N/mm on 1000 mm); counterweight force = 2 × T3 = 19.23 kN
- This reproduces the Rulmeca worked example (Fu 2377 daN, T1 3430 daN, Tg 1922 daN; 1 daN = 10 N).
Assumptions and limits
- One straight section with a head drive and a tail gravity take-up. Other layouts change T2, T3 and the counterweight.
- Cq, Ct and f are cited default coefficients — change them for your conveyor. Use f 0.023–0.027 for dusty, overloaded or poorly maintained conveyors.
- μ is not a fixed property: verify it for your lagging, wet or dirty conditions. Too high a μ underestimates the take-up.
- Not included: start-up and braking forces, skirtboard, scraper and plough resistances, multiple drives, vertical curves and downhill (regenerative) conveyors. A negative Te is refused.
- The counterweight mass shown is the force ÷ g; add for carriage, pulley and rope friction in the real take-up.
- Confirm the design with a full method such as ISO 5048, DIN 22101 or CEMA before buying a belt, motor or counterweight.
Screening estimate, not a design approval. Verify measured inputs, current standards, manufacturer limits and site procedures before purchasing, cutting or installation. Isolate and lock out equipment before any hands-on measurement.
Questions
Why does the sag minimum often govern?
On short, lightly inclined conveyors the drive needs only a small slack-side tension, but the belt still needs enough tension to stay within the sag limit between idlers. The take-up must provide the higher of the two.
What do I do with T1?
Use it as the maximum belt tension in the belt rating check, with your approved safety factor and splice efficiency.
Can I use this for a downhill conveyor?
No. When Te is negative the conveyor drives the motor and needs a braking and regeneration check, which this tool does not do.
Source notes
- Rulmeca, Rollers and Components for Bulk Handling, Technical Information: tangential force, Cq/Ct/f coefficients, wrap factor, 2 % sag minimum and gravity take-up (method used with credit; coefficient tables summarised, not reproduced).
- Euler–Eytelwein (capstan) relation for drive slip. Full methods for comparison: ISO 5048, DIN 22101, CEMA Belt Conveyors for Bulk Materials.
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