Conveyor belt length calculator (two pulleys)
Exact pitch-line length of an open belt around two pulleys, from the centre distance and both pulley diameters.
Result
How it works
For a simple two-pulley conveyor, the belt follows two straight spans (the common tangents) and an arc of contact on each pulley. This calculator uses the exact geometry, so it also works when the head and tail pulleys have different diameters.
It gives the geometric length only. A real belt order also needs the extra length for snub and bend pulleys, take-up travel and the splice, so use this as the starting figure, not the order length.
Formula
Δ = |D₁ − D₂| / 2 L = 2√(C² − Δ²) + π(D₁ + D₂)/2 + 2Δ · asin(Δ / C) All lengths in mm; result ÷ 1000 gives metres. For equal pulleys: L = 2C + πD.
| Symbol | Meaning | Unit |
|---|---|---|
| L | Endless belt length on the pitch line | m |
| C | Centre distance between the two pulleys | mm |
| D₁, D₂ | Effective pitch diameter of each pulley | mm |
| Δ | Half the difference of the two diameters | mm |
Worked example
Inputs: Pulley centre distance C = 10000 mm; Pitch diameter D₁ = 500 mm; Pitch diameter D₂ = 500 mm.
- Equal pulleys, so Δ = 0 and L = 2C + πD
- 2 × 10,000 + π × 500 = 20,000 + 1,570.8 = 21,570.8 mm
- L ≈ 21.571 m
Assumptions and limits
- Two open (uncrossed) pulleys only. Snub, bend and take-up pulleys are not included.
- Enter effective pitch diameters (pulley shell + lagging + about half the belt thickness), not automatically the bare drum diameter.
- Excludes splice allowance, take-up travel and elastic stretch. Do not use the result directly as a belt order length.
- The centre distance must be greater than the sum of the two pulley radii.
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
What diameter should I use?
Use the pitch diameter: the shell diameter plus lagging on both sides plus roughly one belt thickness. Using the bare shell diameter underestimates the length.
Why is my belt order longer than this?
Orders add take-up travel, splice length and the extra path around snub or bend pulleys. This tool gives the two-pulley geometry only.
Source notes
- Derived from the two common external tangents and the pulley contact arcs (standard open-belt geometry).
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