Belt Length Calculator
Find the belt length for a two-pulley drive. Enter the center distance and both pulley diameters (inches, mm, or cm) to get the required belt length, the wrap angle on the small pulley, and the length in alternate units.
Example: with Center distance (C) 12 · Large pulley diameter (D) 6 · Small pulley diameter (d) 3 · Units inches → Belt length: 38.32 in (973.4 mm).
- In other units97.34 cm (3.19 ft)
- Wrap angle (small pulley)165.6° on small pulley
Computed by the calculator below using its default values. Change any input to see your own numbers.
The belt wraps each pulley plus spans the gap twice. The (D-d)^2/(4C) term corrects for the pulleys being different sizes; when they are equal it vanishes.
What the formula captures
A belt around two pulleys does three things: it wraps partway around each pulley, and it spans the open gap between them twice. Add those up and you get the standard open-belt length: two center distances, plus half the circumference of the combined pulley diameters, plus a small correction for the size difference. That correction, (D minus d) squared over four times the center distance, accounts for the belt angling slightly as it crosses from a big pulley to a small one.
When both pulleys are the same size the correction disappears and the belt is simply two spans plus one full pulley circumference.
From calculated length to a real belt
This gives the theoretical length along the belt's path. Real V-belts and serpentine belts are sold in standard stock lengths measured at a pitch line inside the belt, so your calculated figure will land between two catalog sizes. Round to the nearest available belt and rely on the tensioner or adjustable center distance to take up the difference. The wrap angle matters too - too little wrap on the small pulley and the belt can slip, which is why idlers exist.
How it’s calculated
Open-belt length L = 2C + (pi/2)(D + d) + (D - d)^2 / (4C), where C is center distance and D, d are the large and small pulley diameters (outside diameters). Wrap angle on the small pulley = 180 - 2 x arcsin((D - d) / (2C)) degrees. Unit conversions use 1 in = 25.4 mm exactly; 1 ft = 12 in.
Assumes a simple open belt around two round pulleys using outside diameters. Real belts use a pitch diameter and standard stock lengths, so round up to the nearest available belt.
Belt length vs. center distance (6 in and 3 in pulleys)
| Center distance C | Belt length L |
|---|---|
| 8 in | 30.42 in |
| 10 in | 34.36 in |
| 12 in | 38.32 in |
| 14 in | 42.30 in |
| 16 in | 46.28 in |
Computed with L = 2C + (pi/2)(D+d) + (D-d)^2/(4C), D = 6 in, d = 3 in.
Common mistakes
- Mixing units - all three lengths (C, D, d) must use the same unit.
- Using radius instead of diameter, which shrinks the wrap term by half.
- Expecting the exact number to be a stock belt; catalog belts come in fixed lengths.
- Ignoring wrap angle - a tiny small-pulley wrap invites slip and squeal.
Frequently asked questions
What is the belt length formula?
For an open belt on two pulleys, L = 2C + (pi/2)(D + d) + (D - d)^2/(4C), where C is the center distance and D and d are the large and small pulley diameters. All values must share the same unit.
Do I use diameter or radius?
Diameter. The formula is written for pulley diameters; using radius will roughly halve the pulley-wrap term and give a belt that is far too short.
Why does my number fall between belt sizes?
Belts are manufactured in standard lengths measured along an internal pitch line. Round to the nearest available size and use a tensioner or adjustable mount to absorb the small difference.
What is wrap angle and why does it matter?
Wrap angle is how much of the small pulley the belt hugs. Less contact means less grip, so a low wrap angle (from a big size difference or short center distance) can cause slipping; an idler pulley increases it.
Does this work for crossed belts?
No. This is the open-belt formula. A crossed belt uses a plus sign on the size term and wraps more of each pulley, giving a different length.