How it works
For a two-pulley open (non-crossed) drive, the belt length is L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)² / (4C) where C is the centre distance and D₁, D₂ are the small and large pulley diameters. The first term is the two straight spans, the second is the half-wrap around each pulley, and the third corrects for the slight angle of the belt between pulleys of different size.
The wrap (contact) angle on the small pulley is
θ₁ = 180° − 2·asin((D₂ − D₁)/(2C)), and the large pulley gets the
rest, θ₂ = 360° − θ₁. The small pulley always wraps less, so it
limits grip: keep θ₁ above roughly 120° to avoid slip.
Worked example
A centre distance C = 300 mm with a 100 mm small pulley and a 200 mm large
pulley gives
L = 2·300 + (π/2)(100+200) + (200−100)²/(4·300) ≈ 1080 mm. The
small-pulley wrap is ≈ 161° and the large-pulley wrap
≈ 199°. The calculator returns exactly these values.
Frequently asked questions
- How do I calculate belt length?
- For a two-pulley open drive, belt length L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), where C is the centre distance and D₁, D₂ are the pulley diameters. Enter the three values above and the calculator solves it.
- What belt length do I need for two pulleys?
- Use L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C). It adds the two straight spans (≈ 2C) to the parts of the belt wrapped around each pulley. Round the result up to the nearest standard belt size.
- What is the wrap (contact) angle and why does it matter?
- The wrap angle is how far the belt contacts each pulley. The smaller pulley always has the smaller wrap, so it limits grip: less contact means less friction and a higher chance of slip. Keep the small-pulley wrap above about 120° — reduce the speed ratio or add an idler if it falls below that.
- Does this work for V-belts and timing belts?
- Yes — use the pulley pitch diameters (not the outside diameters) and the result is the belt pitch length. Then round to the nearest standard belt and adjust the centre distance to suit the belt you pick.
- What about a drive with three or more pulleys?
- This tool covers the two-pulley open drive. For three or more pulleys (or a serpentine/idler layout) you sum the straight segments and the wrap arcs around each pulley individually — that wrap-by-wrap geometry is beyond this calculator.
- Does it work in metric and imperial?
- Yes — enter the centre distance and diameters in mm or inches; the belt length and wrap angles convert. Toggle SI/Imperial in the header.
Method & assumptions
- Open (non-crossed) belt on two parallel pulleys — not a crossed belt or a multi-pulley/serpentine layout.
- Use the pulley pitch diameters; for V-belts and timing belts the result is the belt pitch length.
- Round the length up to the nearest standard belt, then set the centre distance from the belt you choose (most drives need an adjustable centre or a tensioner).
Related calculators
- Pulley Calculator — Pulley ratio, driven RPM and belt speed from pulley diameters.
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- Chain Length Calculator — Roller-chain length in links and mm from sprocket teeth and center distance.
- Bearing Life (L10) Calculator — Basic L10 rating life in revolutions and hours from load, speed and rating.