Belt length calculator for two pulleys
This belt length calculator works out the length of a V-belt on two pulleys from their diameters and the center distance – or the center distance for a belt you already have. It uses Gates’ formula L = 2C + 1.57 (D + d) + (D − d)² ÷ 4C: an 8-inch and a 4-inch pulley 16 inches apart need a 51.09-inch belt.
Example: Calculate: belt length from center distance · Units: inches · Large pulley diameter (D) 8 · Small pulley diameter (d) 4 · Center distance (C) 16 · Speed of the small pulley 1,750 rpm → Result: Belt length 51.09 in. Source: Gates – Heavy Duty V-Belt Drive Design Manual, p. D8 Formula No. 3: belt length = 2C + 1.57 (D + d) + (D − d)² / 4C (read 09.10.2026). Updated: .
How it is calculated
L = 2C + 1.57 (D + d) + (D − d)² ÷ 4C. C is the center distance, D the large and d the small pulley diameter. This is Formula No. 3 in the Gates Heavy Duty V-Belt Drive Design Manual. The 1.57 is π ÷ 2, the half circumference around both pulleys; the last term adds the extra length when the pulleys differ in size.
Examples
| Pulleys | Center distance | Belt length |
|---|---|---|
| 8 in and 4 in | 16 in | 51.09 in |
| 12 in and 3 in | 20 in | 64.56 in |
| 200 mm and 100 mm | 400 mm | 1277.3 mm |
| 300 mm and 100 mm | 400 mm | 1453.0 mm |
Center distance from belt length
Solving the same formula for C gives C = (B + √(B² − 2 (D − d)²)) ÷ 4 with B = L − 1.57 (D + d). A 52-inch belt on 8-inch and 4-inch pulleys sits at 16.46 inches. Gates recommends choosing the next standard belt length above the calculated value and then working out the actual center distance – which is what the second mode does.
Speed ratio and wrap angle
Without slip the large pulley turns at n × d ÷ D: a 4-inch motor pulley at 1750 rpm drives an 8-inch pulley at 875 rpm. The wrap angle on the small pulley is 180° − 2 × asin((D − d) ÷ 2C), 165.6° in the first example. For gears use the gear ratio calculator; for bicycle chains the bike chain length calculator.
Frequently asked questions
How do you calculate belt length for two pulleys?
L = 2C + 1.57 (D + d) + (D − d)² ÷ 4C. For 8 in and 4 in pulleys 16 in apart: 32 + 18.84 + 0.25 = 51.09 in.
How do I find the center distance for a belt I have?
Use the second mode. A 52 in belt on 8 in and 4 in pulleys gives a center distance of 16.46 in.
Which diameter do I enter?
The pitch (datum) diameter for classic V-belts; Gates uses the outside diameter for some belt types. Take it from the pulley catalog.
What if both pulleys are the same size?
Then L = 2C + 3.14 × D. Two 150 mm pulleys 300 mm apart need a 1071 mm belt.
How do I calculate the driven speed?
Driven rpm = driver rpm × driver diameter ÷ driven diameter: 1750 × 4 ÷ 8 = 875 rpm.
Is the result exact?
It is the standard design formula; the belt you buy comes in standard lengths, so choose the next size and allow for tensioning.
Sources and legal basis
As of: · Editorial policy
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