Enter the two pulley diameters and the centre distance and get the belt length, the speed ratio and the belt speed. Or enter a belt length and get the centre distance it gives. For an open drive, where both pulleys turn the same way.
Worked example
These are example values. Change any entry above and press Calculate to run your own numbers.
Belt length (open belt)
1,759.15 mmL = 2C + π(D + d) ÷ 2 + (D − d)² ÷ 4C
Centre distance
600 mm
Speed ratio (large ÷ small)
2.5 : 1
Belt wrap on the small pulley
165.6° drive ratings assume enough wrap, commonly 120° or more
Large pulley speed (no slip)
700 rpm
Belt speed
9.163 m/s (1,804 ft/min)
Use pitch diameters for V-belts and timing belts, and the belt maker's standard lengths and tension data to choose a real belt. The nearest standard belt length will differ from the calculated one, and the centre distance is then adjusted.
How it works
A belt on two pulleys wraps part of each and runs straight between them. The length is the two straight spans plus the two arcs of wrap. The standard approximation below is accurate for ordinary centre distances and is what belt makers and catalogues use for a first selection. The belt you buy comes in standard lengths, so use the result to choose the nearest one and adjust the centre distance with the take-up.
The formulas
Belt length L = 2C + π ÷ 2 × (D + d) + (D − d)² ÷ (4C)
Centre distance C = (b + √(b² − 8 × (D − d)²)) ÷ 4, where b = L − π ÷ 2 × (D + d)
Speed ratio = D ÷ d
Belt speed = π × d × small pulley rpm
D large pulley diameter, d small pulley diameter, C centre distance, all in the same unit
Frequently asked questions
How do you calculate the length of a belt for two pulleys?
Use L = 2C + π ÷ 2 × (D + d) + (D − d)² ÷ (4C). For a 250 mm and a 100 mm pulley at 600 mm centres, that is 1,200 + 549.8 + 9.4 = about 1,759 mm.
Is this the pitch length or the outside length?
It is the length measured on the diameters you enter. For a V-belt use the pitch diameters of the pulleys and you get the pitch length, which is the length belts are sold by. Use the diameters at the belt's pitch line for a timing belt too.
Does it work for a crossed belt?
No. A crossed belt, where the pulleys turn opposite ways, has a different wrap and a different formula. This calculator is for an open drive only.
How do I find the centre distance for a standard belt?
Choose the mode that takes the belt length, enter the standard length and the two diameters, and the calculator returns the centre distance that belt gives. If the belt is too short to wrap both pulleys it says so rather than returning a number.
How much take-up should the drive have?
It depends on the belt type and length, and the belt maker's catalogue gives the allowance for installation and for stretch. Leave adjustment in the motor base so the belt can be fitted without forcing it and tensioned afterwards.
