Belt Length Calculator

Belt Length for Two-Pulley Drives

A flat or V-belt connecting two pulleys must wrap each sheave and span the center distance between shafts. The open-belt formula applies when both pulleys rotate in the same direction. The crossed-belt formula applies when the belt twists so the pulleys rotate in opposite directions.

Open Belt Formula

For same-direction rotation:

$$L = 2C + \frac{\pi(D + d)}{2} + \frac{(D - d)^2}{4C}$$

Where $D$ is the large pulley diameter, $d$ is the small pulley diameter, and $C$ is the center distance (all in the same length units).

Crossed Belt Formula

For opposite-direction rotation, replace the correction term:

$$L = 2C + \frac{\pi(D + d)}{2} + \frac{(D + d)^2}{4C}$$

Related tools: Pulley Calculator and Gear Ratio Calculator.

Frequently Asked Questions

When should I use the open vs crossed belt formula?

Use the open formula when both pulleys turn the same way with a single belt loop. Use the crossed formula when the belt crosses between pulleys so they rotate in opposite directions.

Do pulley diameters include the belt seating depth?

Yes. Use the pitch diameter or effective diameter where the belt actually runs, not the outside rim of the pulley flange.

What units should I use?

Keep $D$, $d$, and $C$ in the same unit. Millimeters are common in mechanical drawings; the calculator reports belt length in millimeters.

Why is the correction term different for crossed belts?

A crossed belt wraps more tightly around the pulleys because the belt must cross between shafts. The $(D+d)^2/(4C)$ term accounts for that extra wrap length.

Report

Belt Length for Two-Pulley Drives

Open Belt Formula

Crossed Belt Formula

Frequently Asked Questions

Related Tools

Recent Visits

Finance Calc Kit