Find the required open-belt length from your pulley diameters and center distance, plus the nearest standard belt size and contact angle.
Enter both pulley diameters and the center distance between them to get the required belt length.
Enter your details and hit calculate
Belt drives are one of the simplest and most widely used ways to transmit rotational power between two shafts that aren't directly coupled, found everywhere from small workshop motors and compressors to large conveyor systems and HVAC fans. Before a belt can be ordered or fabricated, its exact length must be known, since belts are manufactured in fixed standard lengths and an incorrectly sized belt will either run too loose, causing slip and premature wear, or too tight, causing excessive bearing load and shortened belt and pulley life.
The calculation accounts for three geometric contributions that together make up the belt's total path: twice the center distance, the wrap contribution from both pulley circumferences, and a correction term for the difference in pulley diameters. The standard open-belt-drive formula combines these into a single practical equation using the two pulley diameters and the center distance.
Contact angle. Beyond the length itself, this calculator also estimates the belt's wrap (contact) angle on the smaller pulley, since a small contact angle reduces the effective grip and torque-carrying capacity of the drive. As a rough guide, a contact angle below about 150° on the smaller pulley is often a sign the center distance is too short relative to the diameter difference, and may call for a larger center distance or an idler pulley.
This calculator is used constantly when replacing a worn belt where the original length specification has been lost, when designing a new belt drive from scratch, or when changing a pulley size on an existing drive. The nearest standard belt size shown alongside the raw calculated length saves a manual lookup against a belt size chart.
Example: Motor pulley D1 = 100 mm, fan pulley D2 = 300 mm, center distance C = 500 mm. Belt Length = 2(500) + 1.57×(400) + (200)² ÷ 2000 = 1000 + 628 + 20 ≈ 1648 mm. The nearest standard belt size at or just above this value should be selected, and the contact angle on the smaller pulley works out to roughly 157°, which is within the comfortable range for reliable grip.
Reference: The open-belt-length formula and contact-angle relationship are standard equations used across mechanical engineering handbooks for flat and V-belt drive design. This calculator is for preliminary, educational sizing only and does not replace a manufacturer's belt selection chart.
The pitch-length formula used here is the standard open-belt-drive geometry equation and applies closely to flat belts and V-belts measured at their pitch (effective) diameter. Timing belts must match a fixed tooth pitch exactly, so treat the result as a starting estimate and round to the nearest available toothed belt length rather than any arbitrary standard size.
When D1 equals D2, the (D2 − D1)² term becomes zero and the formula simplifies to L = 2C + 1.57(D2 + D1), which is just twice the center distance plus the combined circumference contribution — the belt wraps both pulleys equally with a full 180° contact angle on each.
The contact (wrap) angle determines how much friction area the belt has on the smaller pulley, which directly limits the torque it can transmit before slipping. A short center distance relative to the diameter difference reduces this angle; if it drops much below 150°, consider increasing the center distance, using an idler pulley, or switching to a toothed/timing belt that doesn't rely on friction.
Belts are manufactured in fixed increments (commonly every 25 mm or specific inch-based sizes depending on belt type). This calculator rounds the raw calculated length up to the nearest 25 mm as a general-purpose estimate — always confirm against your specific belt manufacturer's standard length chart before ordering.
No — this is a preliminary, educational length and geometry estimate. A complete belt drive design should also account for belt type and cross-section, required power rating, service factor, number of belts (for multi-belt drives), and manufacturer-specific pitch length tables.