Belt Length Calculator — Open & Crossed Drive Belts
Enter the two pulley diameters and the centre-to-centre distance to get the exact belt length, wrap angles on each pulley and the proportion of belt in each arc and straight section.
Belt type
mm
mm
mm
Exact open/crossed belt length using arc + straight-run geometry
- 1
Offset angle α
arcsin((100 − 50) ÷ 500) = 5.739°Angle by which the belt diverges from the pulley centre-line. - 2
Arc on large pulley
100 × (π + 2 × 0.1002) = 334.19 mm - 3
Arc on small pulley
50 × (π − 2 × 0.1002) = 147.06 mm - 4
Straight run (total)
2 × 500 × cos(5.739°) = 994.99 mm - 5
Belt length L
334.19 + 147.06 + 994.99 = 1,476.2 mm
How does this calculator work?
Open belt length L = R(π + 2α) + r(π − 2α) + 2C·cos α, where α = arcsin((R − r)/C), R and r are pulley radii (mm), C is centre distance (mm). For crossed belts use β = arcsin((R + r)/C) with both wrap angles > 180°. Speed ratio = D₁/D₂.
Formula
How this is calculated
A flat or V-belt drive consists of two pulleys connected by a belt that wraps around an arc of each pulley and runs straight between them. For an open belt (both pulleys rotate in the same direction) the geometry gives two unequal arcs: the large pulley has a wrap angle greater than 180° and the small pulley less than 180°. The critical angle α = arcsin((R − r) / C) describes how much the belt diverges from the centre-line, where R and r are the pulley radii and C is the centre distance. The exact belt length is L = R(π + 2α) + r(π − 2α) + 2C·cos α.
For a crossed belt (pulleys rotate in opposite directions) the belt crosses between the pulleys, giving both pulleys a wrap angle greater than 180°. The formula becomes L = (R + r)(π + 2β) + 2C·cos β, where β = arcsin((R + r) / C). A crossed belt requires the centre distance to exceed the sum of the radii.
The speed ratio is D₁ / D₂: if the large pulley drives a smaller one the output spins faster (step-up). The wrap angle on the small pulley determines traction — shorter wrap means less grip and earlier slipping, so a ratio much above 3:1 or a very short centre distance may require a tensioner.
Frequently asked questions
In an open belt both pulleys rotate in the same direction. The belt wraps the top of one pulley and the bottom of the other. In a crossed belt the belt crosses between the pulleys, making them rotate in opposite directions. Crossed belts generate more wrap angle on both pulleys but the belt wears faster at the cross-point.
The belt transmits torque only over the arc in contact with each pulley. A small wrap angle means fewer belt fibres are gripping, reducing the maximum power the drive can transmit before slipping. A wrap angle below about 120° (π − 2α < 2.09 rad) is generally considered marginal — increase centre distance or use a tensioner.
The length formula applies equally to flat belts, V-belts and synchronous (toothed) belts — all use the same arc-plus-straight-run geometry. For V-belts, use the pitch diameter (slightly smaller than the outer diameter) rather than the outer diameter, as the belt rides in the groove at a smaller effective radius.
TG we-Calculate Editorial Team. (2026). Belt Length Calculator — Open & Crossed Drive Belts [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/belt-length-calculator
TG we-Calculate Editorial Team. "Belt Length Calculator — Open & Crossed Drive Belts." TG we-Calculate. 2026. https://we-calculate.com/calculator/belt-length-calculator.
TG we-Calculate Editorial Team, "Belt Length Calculator — Open & Crossed Drive Belts," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/belt-length-calculator
@misc{wecalculate_belt_length_calculator, title = {Belt Length Calculator — Open & Crossed Drive Belts}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/belt-length-calculator}}, year = {2026}, note = {TG we-Calculate} }
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