EngineerBenchFinding belt length or pulley center distance
Belt length depends on both pulley pitch diameters, the distance between their shaft centers, and whether the belt is open or crossed. The calculation follows the straight spans and pulley contact arcs. It can also solve for center distance when a belt's pitch length is known.
Measure along the same reference
Match pitch diameters with pitch length. An inside-length or outside-length belt marking is not automatically the length used here. Check the belt series before transferring a catalog length into the center-distance mode.
Leave room to fit and tension the belt
The geometric length does not include installation travel, a tensioner's movement, or belt stretch. Use it to narrow the catalog choices, then check the chosen belt's installation allowance. This two-pulley model does not include idlers or a multi-pulley routing.
Checking a catalog belt against the layout
Center distance is measured between shaft axes. It is not the free distance between pulley rims. The straight portions of a belt meet the pulleys tangentially, so their lengths depend on pulley size as well as shaft spacing. An open belt and a crossed belt have different tangent geometry and wrap; selecting the wrong arrangement can give a plausible-looking but unsuitable length.
For a proposed drive, calculate the geometric pitch length and compare it with available belts of the correct section. Then use the center-distance mode with a candidate catalog length to see where the shafts would need to sit. Repeat for adjacent catalog sizes if the motor mount has a limited adjustment range. The inverse calculation only solves the geometric relationship: it does not reserve travel for installing the belt or set the correct working tension. Check that the physical pulley spacing remains possible throughout adjustment and that the belt manufacturer permits the selected routing.
Formula
Uses exact tangent and arc geometry for two circular pulleys. Center distance is solved numerically.