Belt Length Calculator
Enter both pulley pitch diameters and the center distance to get the belt pitch length in mm and inches, plus the speed ratio.
Last updated: 2026-09-15
How the calculation works
- The belt wraps two straight runs plus arcs on each pulley; the classical open-belt equation collapses that geometry into one formula.
- Use pitch diameters for V-belts (roughly the groove's effective depth) and outer diameter for flat belts.
- The speed ratio comes from the diameter ratio, identical logic to gears.
Formula
L = 2C + π(D + d)/2 + (D − d)² / (4C)
| Symbol | Meaning | Unit |
|---|---|---|
L | Belt pitch length | mm |
C | Center distance | mm |
D, d | Large and small pitch diameters | mm |
Worked example
Interpreting the result
Order the nearest standard belt designation — V-belts come in fixed pitch lengths. If the belt is significantly shorter than calculated, it won't fit around both pulleys; much longer and the tensioner may run out of adjustment. The (D−d)² term shows that large diameter differences demand longer belts for the same center distance.
Assumptions
- Open (non-crossed) belt drive, both pulleys in the same plane.
- Rigid pulleys, no belt slip or creep.
Limitations
- Timing belts use pitch (tooth) length — use the manufacturer's pitch-line calculation instead.
- Jockey/idler pulleys and serpentine paths are not modeled.
- Does not check minimum wrap angle (keep ≥120° on the small pulley for V-belts).
Frequently asked questions
Should I measure the old belt instead?
A worn belt has stretched — measuring it overestimates. Use the geometry calculation, then select the closest standard belt; tensioners absorb the small difference.
What is pitch diameter?
For V-belts it's the effective diameter at the belt's neutral axis in the groove — slightly larger than the groove bottom, smaller than the outer edge. Manufacturers publish pulley pitch diameters.