Belt Length Calculator

An open belt over two pulleys runs along the two outer tangents and wraps each pulley. With diameters D1, D2 and center distance C:

L = 2C + π(D1 + D2)/2 + (D1 − D2)² / (4C)

Worked example. D1 = 100 mm, D2 = 200 mm, C = 500 mm → L = 1000 + 471.24 + 5 = 1476.24 mm. The first term is the two straight runs, the second the wrap around both pulleys, and the last corrects for the belt crossing between pulleys of different size. That term stays small until the diameters differ a lot relative to the center distance.

It works in either direction. Give it both diameters and the center distance and it returns the belt length; give it both diameters and a belt length and it solves for the center distance instead. Fill all four and it checks them against each other and flags a mismatch over 1%.

Center distance is the dominant term, so measure it carefully: a millimetre there moves the belt length about two millimetres, while a millimetre of pulley diameter moves it only about 1.6.

With a tensioner. An idler pressing on the free run lengthens the belt, and the formula above no longer covers it. The calculator then traces the belt exactly: three straight runs plus the arc it wraps on each pulley. Deflection is how far the tensioner pushes the belt out of its straight line. An inside tensioner sits in the loop and pushes outward; a backside one presses on the back of the belt from outside. Position is measured along the belt from Pulley 1; leave it blank for the midpoint, which gives the shortest belt for a given deflection. It still solves for center distance in reverse, and with the center distance and the belt length both known it solves the deflection instead: how far the idler must push to take up a standard belt.

The drawing follows the inputs to scale. The dashed line is the belt run without the tensioner, so the deflection reads against it. A layout that cannot be built is still drawn, with the part at fault in red.