Belt Length & Pulley Calculator
Belt length, wrap angle and centre distance for open and crossed drives.
How it works
For an open drive the belt runs along two tangents and wraps part of each pulley, which gives
L = 2C + (π ÷ 2)(D₁ + D₂) + (D₁ − D₂)² ÷ 4C
The last term corrects for the fact that the tangent lines are not quite parallel. It matters when the pulleys differ greatly in size and almost vanishes when they are similar — at equal diameters it is exactly zero and the formula collapses to two straight runs plus one full circumference.
A crossed belt uses the same expression with that sign flipped to a sum, because it wraps more of both pulleys. It also rubs against itself where it crosses, which is why it survives only on slow, low-power drives.
Wrap angle on the small pulley is what limits the power a friction drive can transmit — it is the shorter contact and the steeper tension gradient. Below about 120° a V-belt starts slipping under load, and the fix is a larger centre distance or an idler pushed into the slack side. Toothed belts do not care, because they do not rely on friction, but they still want three or four teeth in mesh.
Belt speed is worth a glance. Ordinary V-belts are happy to about 25 m/s and start throwing heat and losing life above it.
Common questions
Which diameter do I measure?
Pitch diameter, not outside diameter. On a V-belt pulley the belt sits down in the groove, so the pitch diameter is a few millimetres smaller than the rim — the manufacturer publishes it. On a toothed pulley it is teeth × pitch ÷ π.
My belt length isn't a size anyone sells.
Pick the nearest stock length and solve back for the centre distance — that is what the second mode is for. Then give yourself adjustment: a slotted motor base or a tensioner, because belts stretch during their first hours of running.
What wrap angle do I need?
180° is ideal and only happens with equal pulleys. Keep the small pulley above 120° for a V-belt. Below that, increase the centre distance or add an idler on the slack side pressing inward.
Does the ratio depend on the belt?
No. Speed ratio is purely the diameter ratio, and only slip changes it. A toothed belt has no slip at all, which is why cam drives and printer axes use them.