How to use it
- Type the Driver pulley diameter d1, mm and the Driven pulley diameter d2, mm.
- Type the Centre distance C, mm between the two axles and the Driver speed N, rpm.
- If the belt is thick or the drive slips, type the Belt thickness t, mm and the Belt slip s, %. Otherwise leave them at 0.
- Read the Open belt length L, mm, the two wrap angles and the Driven pulley speed, rpm, then open Working, step by step.
The open belt length
For an open belt the length is made of two straight spans and two arcs of belt on the pulleys. With α the half-angle of the geometry, the straight spans are 2 × C × cos α and the arcs add up to π × (d1 + d2) ÷ 2 + α × |d2 − d1|. The approximate form from the NPTEL notes is close to the exact one for ordinary drives.
α = sin⁻¹(|d2 − d1| ÷ (2 × C))
L = 2 × C × cos α + π × (d1 + d2) ÷ 2 + α × |d2 − d1|
Approximately: L = π × (d1 + d2) ÷ 2 + 2 × C + (d2 − d1)² ÷ (4 × C)Wrap angles and speed
The wrap angle is the part of each pulley that the belt touches. The larger pulley has the larger wrap, 180° + 2α, and the smaller pulley has 180° − 2α. The speed ratio uses the diameters with the belt thickness added, and one minus the slip.
Wrap on the larger pulley: 180° + 2α
Wrap on the smaller pulley: 180° − 2α
Velocity ratio = N_driven ÷ N_driver = (d1 + t) × (1 − s) ÷ (d2 + t)
N_driven = N_driver × velocity ratioWhat this calculator does not include
- Crossed belts, which use another length formula.
- The power a belt carries and the belt tension, which need the belt's own data.
- Idler pulleys and drives with more than two pulleys.
Worked example: 100 mm driver, 300 mm driven, 400 mm apart, 1450 rpm
The half-angle is α = sin⁻¹((300 − 100) ÷ (2 × 400)) = sin⁻¹(0.25) = 14.478°, which is 0.25268 rad. The two straight spans are 2 × 400 × cos α = 774.6 mm and the two arcs are π × 400 ÷ 2 + 0.25268 × 200 = 678.85 mm, so the open belt length is L = 774.6 + 678.85 = 1,453.5 mm.
The wrap is 180° − 2 × 14.478° = 151.04° on the driver, which is the smaller pulley, and 180° + 2 × 14.478° = 208.96° on the driven pulley. With no slip and no belt thickness the velocity ratio is 100 ÷ 300 = 0.3333, so the driven pulley turns at 1450 × 0.3333 = 483.3 rpm.
| Figure | Value |
|---|---|
| Open belt length L | 1,453.5 mm |
| Wrap angle on the driver | 151.04° |
| Wrap angle on the driven pulley | 208.96° |
| Velocity ratio | 0.3333 |
| Driven pulley speed | 483.3 rpm |
Frequently asked questions
Why does the belt need to be longer when the centre distance grows?
A longer centre distance gives longer straight spans of belt between the pulleys. The length grows with twice the centre distance, so a drive with a longer span needs a longer belt.
What is the shortest centre distance I can use?
The centre distance must be more than half the difference of the two diameters, because the sine of the half-angle cannot be above 1. The calculator refuses a shorter distance, since the belt could not wrap round the pulleys.
Why does the driven pulley turn slower than the diameter ratio says?
The belt slips a little, so the driven pulley turns slightly slower than the ideal ratio. Type the slip percentage to include that loss in the speed.
What is the difference between an open and a crossed belt?
An open belt keeps both pulleys turning the same way. A crossed belt twists between the pulleys and reverses the direction. It needs a different length formula, which this calculator does not use.
Why is the belt thickness used in the speed but not in the length?
The speed ratio uses the NPTEL form, in which the belt thickness is added to each pulley diameter. The length uses the pulley diameters as you type them, so enter the pitch diameters if you have them.
Are my numbers sent to a server?
No. The calculation runs in your browser, and nothing you type is stored or sent to us.
Sources
Figures and text last checked on Thursday, November 12, 2026.