Belt Length Calculator
A belt drive transmits rotational power between two shafts using a flexible loop of material running around two pulleys. To cut or order the correct belt you need to know the total belt length, which depends on the diameter of each pulley and the distance between their centre lines. There are two standard configurations. In an open belt drive both pulleys rotate in the same direction. The belt runs along the outside of both pulleys, crossing no imaginary centreline, and the arc of contact on the smaller pulley is reduced when the pulleys differ greatly in size. In a crossed belt drive the belt twists in the space between the pulleys so that the shafts rotate in opposite directions. The crossing gives a larger arc on both pulleys, which increases the grip and the torque that can be transmitted, but also causes extra belt wear at the crossing point. This calculator uses the exact geometric formula for each configuration. You enter the diameter of the larger pulley (D1), the diameter of the smaller pulley (D2), and the centre distance between the two shaft axes. All three values must be in the same unit; enter them in metres and you get the belt length in metres. The tool returns total belt length, the arc of contact on each pulley in degrees, and the half-angle alpha that appears in the formula. Add 1 to 2 percent to the calculated length when ordering belt to allow for pre-tension and stretch.
Add 1 to 2 percent to the calculated length for belt stretch and pre-tension when ordering. Results assume ideal geometry with no belt sag.
How it works
Let R = D1/2 and r = D2/2. For an open belt: alpha = arcsin((R - r) / C). Belt length L = pi*(R + r) + 2*C*cos(alpha) + 2*(R - r)*alpha. Arc on large pulley = pi + 2*alpha (in radians, converted to degrees). Arc on small pulley = pi - 2*alpha. For a crossed belt: alpha = arcsin((R + r) / C). Belt length L = pi*(R + r) + 2*C*cos(alpha) + 2*(R + r)*alpha. Both pulleys have the same arc of contact = pi + 2*alpha. All angles are in radians during calculation and converted to degrees for display.
Worked example
Open belt: D1 = 0.3 m so R = 0.15 m; D2 = 0.1 m so r = 0.05 m; C = 0.5 m. Half-angle alpha = arcsin((0.15 - 0.05) / 0.5) = arcsin(0.2) = 11.54 degrees = 0.2014 rad. Belt length = pi*(0.15 + 0.05) + 2*0.5*cos(0.2014) + 2*(0.10)*0.2014 = 0.6283 + 0.9798 + 0.0403 = 1.648 m. Arc on D1 = (pi + 2*0.2014) * 180/pi = 203.1 degrees. Arc on D2 = (pi - 2*0.2014) * 180/pi = 156.9 degrees.
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