FTC belt calculator

Belt length

Every length here is a pitch length, measured along the line the belt's cords run on. A pulley with $N$ grooves at pitch $p$ has a pitch diameter of

With $D$ the large pulley, $d$ the small one and $C$ the center distance, the belt is two straight spans and two arcs:

That is exact. The shortcut most calculators use is its series expansion, and it drifts as the ratio grows:

Center distance from a belt

Given a belt, the page solves that length for $C$ by Newton's method. Differentiate it and the $\varphi$ terms cancel, which leaves an exact slope:

It starts from the shortcut's answer, falls back to bisection whenever a step would leave the bracket, and stops when the length it reproduces is within $10^{-9}$ mm of the belt.

Checked against Gates

The two drives worked in the Gates PowerGrip GT2 design manual, run through this page and through the shortcut. Lengths and center distances in inches.

The shortcut misses both in the second decimal.

Teeth in mesh

The small pulley, with $N_s$ grooves, is wrapped through

Gates rates its belts at six or more teeth in mesh and takes 20% off the rating for each tooth short of six, so the page flags anything under 6.

Which belt to buy

A belt has a whole number of teeth, so the exact length almost never exists. goBILDA advises rounding up and taking up the slack with a tensioner, because a belt rounded down runs too tight. The pick is the closest belt inside your fit tolerance, otherwise the next longer one.

The tolerance starts at 0.05 mm, the tight end of the 0.05 to 0.08 mm Gates says a fixed-center drive has to hold.

Catalogs

Read from each maker's site on 7 October 2026. A row is only what a product page or listing actually showed, so a size a maker sells can still be missing, and a belt no checked catalog lists reads Not in database.