How it works
An open belt wraps part way around each pulley and runs in two straight spans between them. Adding the straight lengths and the two arcs gives the exact length, which the common approximation 2C + π(D + d)/2 + (D − d)²/(4C) matches closely when the center distance is several times the pulley difference.
The wrap angle on the small pulley is 180° minus twice the angle between the belt and the line of centers. It matters for grip: the smaller the wrap, the less power the belt can carry.
Worked example
An 8 in and a 4 in pulley on 20 in centers, with the small pulley at 1,750 RPM:
- Approx. length = 2 × 20 + π ÷ 2 × (8 + 4) + (8 − 4)² ÷ (4 × 20) = 59.05 in
- Exact geometry: length = 2√(C² − ((D − d) ÷ 2)²) + ½ × (D × (π + 2β) + d × (π − 2β)), β = arcsin((D − d) ÷ 2C) = 59 in
- Wrap on the small pulley = 180° − 2β = 168.5°
- Belt speed = π × 4 in × 1,750 RPM ÷ 12 = 1,833 ft/min
| Input | Value |
|---|---|
| Large pulley diameter | 8 in |
| Small pulley diameter | 4 in |
| Center distance | 20 in |
| Small pulley speed | 1750 RPM |
| Result | Value |
|---|---|
| Belt length (pitch length) | 59 in |
| Wrap angle on the small pulley | 168.5 ° |
| Belt speed | 1,833 SFM |
Assumptions and limits
- Open (uncrossed) belt on two pulleys of a single plane; crossed belts and idlers change the length.
- Diameters are pitch diameters for V-belts; use outside diameters for flat belts and pitch line for timing belts.
- Result is the belt’s pitch length; pick the nearest standard belt size and adjust the center distance to suit.
Common questions
How do I calculate the belt length for two pulleys?
Add twice the center distance, π ÷ 2 times the sum of the diameters, and the square of the diameter difference over four times the center distance.
What is the wrap angle?
The arc of the pulley the belt touches. For an open belt it is 180° on equal pulleys and less on the small pulley of an unequal pair.
How do I set the center distance for a standard belt?
Compute the length, choose the nearest standard belt, then slide the motor to the center distance that gives that belt’s length.
What about inside or outside length?
V-belts are sold by nominal length. Use the belt maker’s conversion between pitch length and nominal length.
Sources
- Open-belt length geometry: two tangent spans plus wrap arcs; the (D − d)² ÷ 4C form is the standard machine-design approximation.
- Belt speed = π × diameter × RPM ÷ 12 in ft/min.
Updated 2026-09-30