Belt Length Calculator
The Geometry of Power Transfer
Belts and pulleys are the unsung heroes of mechanical engineering. They allow us to transfer rotational energy from a motor to a machine, often over a distance. But how do you know what size belt to buy?
Using a piece of string to measure around the pulleys is the traditional way, but it is notoriously inaccurate. String stretches, and measuring in a cramped engine bay or machine housing is difficult. A Belt Length Calculator uses the diameters of the pulleys and the distance between their centers to provide a precise mathematical result.
The Standard Belt Formula
For most standard two-pulley systems (open belt drive), engineers use the following formula to estimate the pitch length ($L$):
- C: Center distance between the pulleys.
- D: Large pulley diameter.
- d: Small pulley diameter.
Why "Pitch Diameter" Matters
When measuring your pulleys, don't just measure the outer edges. For the most accuracy, you need the Pitch Diameter.
The pitch diameter is the circle where the neutral axis of the belt travels. On a V-belt, this is usually slightly inside the groove. If you measure the very top of the pulley, your belt will likely arrive slightly too long.
Choosing the Right Type of Belt
The length is the same regardless of the shape, but the application determines the type:
1. V-Belts
The "V" shape allows the belt to wedge into the pulley groove, increasing friction. These are common in automotive fans and air compressors. They are great for high-torque loads but can slip if they get wet or oily.
2. Timing Belts (Synchronous)
These have "teeth" that lock into grooves on the pulley. They cannot slip. These are used when timing is critical, such as connecting a car's crankshaft to the camshaft, or in 3D printers and CNC machines.
3. Flat Belts
Older industrial machinery used wide flat belts. They are efficient and can travel at very high speeds, but they require perfectly aligned pulleys to prevent the belt from sliding off.
The "Arc of Contact" Problem
In systems where one pulley is much larger than the other, the "wrap" around the small pulley is very low. If the belt covers less than 120 degrees of the small pulley, it is likely to slip under load. Our calculator helps you visualize if your center distance is too short, which is the primary cause of pulley slip.