How this calculator works
The straight belt spans are common external tangents to the pitch circles. Unequal pulleys change both tangent length and wrap angle. This geometric result is exact for an ideal thin open belt. Use pitch diameter, rather than flange diameter, and allow for tension adjustment when choosing a standard belt. The inverse is restricted to physically separate pulleys and is solved by bounded bisection.
Formula
Delta = |D1-D2|/2; alpha = asin(Delta/C); L = 2 sqrt(C²-Delta²) + pi(D1+D2)/2 + 2 Delta alpha.
Worked example
Two 200 mm pitch pulleys 1 m apart need a pitch length of 2.628318531 m. Two 100 mm pulleys with a 1.314159265 m belt have a 0.5 m centre distance.
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Frequently asked questions
Does this cover a crossed belt?
No. Crossed belts use internal tangents and a different wrap geometry.
Which diameter should I measure?
Use the diameter at the belt pitch line. Outside flange diameter is usually different.
Why reject touching pulleys?
The model needs two distinct pulleys with room between their pitch circles; it does not model contact or belt thickness.