V-belt length
Belt pitch length from your two sheave diameters and the center distance — plus the small-sheave wrap angle and drive ratio, so you can pick the right belt and check the wrap.
V-belt length · 2, 3 or 4 pulleys · inch or mm
Each pulley: diameter and center position (x, y), in the selected unit
L = 2C + π/2·(D+d) + (D−d)² / 4C
What this gives you
This is the pitch length of a V-belt running on a two-sheave drive, computed from the large and small sheave pitch diameters and the center distance between the two shafts. Pitch length is measured at the belt's pitch line — the datum the belt and sheave standards are built around — so it is the number you match against a catalog belt designation. The governing relation is L = 2C + (π/2)(D + d) + (D − d)² / 4C, where C is the center distance and D and d are the large and small pitch diameters. The calculator also returns the wrap angle on the small sheave and the speed ratio, the two numbers you check right after you have a length.
Pitch length vs. the number on the belt
A V-belt is specified by its pitch (or datum) length, not its outside length, and the difference between the two is a fixed amount set by the cross-section — roughly 0.4 in for an A/4L belt and more for heavier B, C, and 5V sections. The calculated pitch length here will rarely land exactly on a stock length, so round to the nearest standard belt and let the center distance take up the slack. That is why nearly every drive has an adjustable motor base: you set the belt, then move the motor in until the belt seats with the right tension. Size the takeup so you can go about 2 percent shorter for installation and a bit longer for wear.
Field note — watch the wrap angle on the small sheave
Belt grip depends on how far the belt wraps the small sheave, and that angle shrinks as the diameter ratio climbs or the center distance closes. Below about 120° of wrap you start losing usable tension and the belt will slip and glaze under load. If the calculator shows a wrap much under 120°, open the center distance, drop the ratio, or add an idler before you reach for more belt tension — over-tensioning to fix a wrap problem just eats bearings and shafts.
Worked example
A drive with a 12 in large sheave, a 6 in small sheave, and 24 in between centers: 2C = 48, (π/2)(12 + 6) = 28.27, and (12 − 6)²/(4 × 24) = 36/96 = 0.38, so L = 76.65 in. The wrap on the small sheave is 180 − 2 × asin(6/48) = 165.6° — plenty of grip — and the speed ratio is 2.00 : 1. Pick the nearest standard belt to 76.65 in and set the motor base so it seats at that pitch length.