Pulley Belt Size Calculator (Belt Length)

This calculator estimates the length of an open (uncrossed) belt running over two pulleys. Enter the diameters of the large and small pulleys and the distance between their centres; you get the belt length in inches and millimetres.

Formula

L ≈ 2C + π(D + d) ÷ 2 + (D − d)² ÷ (4C).

• D, d: pitch diameters of the large and small pulleys
• C: distance between the pulley centres
• The centre distance must be more than half the sum of the diameters, or the pulleys overlap.

Worked Example

Pulleys of 8 in and 4 in, 20 in apart.

1. 2C = 40
2. π(D + d) ÷ 2 = π × 12 ÷ 2 = 18.8496
3. (D − d)² ÷ 4C = 16 ÷ 80 = 0.2
4. L = 40 + 18.8496 + 0.2 = 59.05 in
5. In millimetres: 59.05 × 25.4 = 1,500 mm

How to read the result

Belts come in set lengths, so choose the nearest standard size and adjust the centre distance (most drives have a sliding motor mount). V-belt sizes are often quoted as an outside length, which is longer than the pitch length this formula gives; check the belt maker’s chart.

Limits and common mistakes

• This is the standard approximation; the exact length uses the wrap angles and differs very slightly.
• A crossed belt is longer: replace (D − d)² with (D + d)².
• Measure centre to centre, not edge to edge.

Frequently Asked Questions

How do I measure a belt I already have?

Wrap a tape around both pulleys along the belt path, or read the size printed on the belt.

What is pitch diameter?

The diameter where the belt actually rides, a little less than the outside diameter of a V-pulley.

What if the pulleys are the same size?

L = 2C + πD.

Can I use metric units?

Yes, enter all three in millimetres and read the inch line as millimetres.

in bd | Large pulley diameter | in | 8 | 0.1 | 200
in sm | Small pulley diameter | in | 4 | 0.1 | 200
in cc | Centre distance | in | 20 | 0.1 | 1000
out blen | Belt length | in | 2 * cc + pi * (bd + sm) / 2 + (bd - sm)^2 / (4 * cc) + 0 * sqrt(cc - (bd + sm) / 2) | 2
out mm | Belt length | mm | blen * 25.4 | 0