Belt Length Calculator
When designing or replacing a belt drive, you need to know the exact belt length for your pulley setup. This calculator uses the standard engineering formula for both open and crossed belt configurations, giving you the belt length, speed ratio, and wrap angles on each pulley.
The standard formula for open belt length is:
L = 2C + (pi/2)(D + d) + (D - d)² / (4C)
Where D is the large pulley diameter, d is the small pulley diameter, and C is the center-to-center distance.
For a crossed belt (where the belt forms an X between pulleys, reversing rotation):
L = 2C + (pi/2)(D + d) + (D + d)² / (4C)
- Speed ratio = D/d. If the large pulley is the driver, the small pulley spins faster by this ratio
- Wrap angle is the contact arc on each pulley. More wrap angle means better grip and less slipping
- The small pulley in an open belt always has a smaller wrap angle, making it the more likely to slip
These formulas are accurate for V-belts, flat belts, and timing belts. For V-belts, manufacturers catalog belts in standard lengths, so round your result to the nearest available size. For timing belts, the length must match the tooth pitch exactly.