A belt drive is the cheapest way to move power between two shafts and change the speed at the same time. Sizing one starts with the belt length: two straight runs between the pulleys, plus the arc the belt wraps around each pulley, plus a small correction because the two pulleys are different sizes. The same geometry hands you the speed ratio (pulley diameters), the belt speed, and the wrap angle on the small pulley — the figure that decides whether the belt grips or slips.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: standard open-belt drive geometry.
The belt-drive equations
C, D and d all carry the same length unit, so the belt length comes out in that unit. The size-difference term is small when the pulleys are similar and grows when they differ, which also pulls the wrap angle down. The driven pulley turns slower than the driver by exactly the diameter ratio — that is the whole point of choosing different pulley sizes.
Worked example — a 2:1 fan drive
Scenario: A 100 mm motor pulley drives a 200 mm fan pulley on 400 mm centers, motor at 1450 rpm.
The drive needs a ~1277 mm belt (round to the nearest standard, then set the center distance to suit). The fan turns at 725 rpm — half the motor speed — and the belt runs at about 7.6 m/s, right in the efficient V-belt band. The small-pulley wrap of 165.6° is generous, so grip is not a concern here.
Frequently Asked Questions
L = 2C + (π/2)(D+d) + (D−d)²/(4C): two straight runs, the wrap around both pulleys, and a size-difference correction.
It equals the pulley diameter ratio. A 100 mm driver on a 200 mm pulley gives 2:1, so the output turns at half speed. N₂ = N₁ × d₁/d₂.
The arc the belt contacts. The small pulley has less wrap and slips first. θ = 180° − 2·arcsin((D−d)/2C); keep it above ~120°.
v = π·d·N (use π·d·N/60 for RPM). Both pulleys share belt speed. Keep V-belts roughly 5–25 m/s.
Open belt: same direction, most common. Crossed belt: opposite direction, slightly longer, wears faster. This tool uses the open-belt formula.