ParrotNotes

Belt Length and Pulley Calculator

Work out the belt length for two pulleys from their diameters and center distance, plus the driven speed, speed ratio and wrap angle. Or start from a belt and get the center distance. Enter pitch diameters in inches or millimeters; the result is the pitch length to look up in the belt maker's catalogue.

Your numbers

The pulley on the motor. Use pitch diameters (datum for classical V-belts); the outside diameter gives an outside length.

Shaft center to shaft center.

rpm

Optional: the motor's nameplate rpm, for the driven speed and the belt speed.

Belt pitch length

–

Speed ratio
–
Driven pulley speed
–
Belt speed
–
Wrap angle
–
Gates' starting center distance
–

This is the pitch length of an open belt. Pick the nearest standard length in the belt maker's catalogue, then set the center distance with the take-up.

Driven speed assumes no slip; a V-belt under load runs slightly slower.

The calculation runs in your browser and ParrotNotes does not store your numbers. They sit in the page address so you can bookmark or share the result.

How belt length is worked out

An open belt is two straight spans and two arcs. The formula adds the spans (about twice the center distance), the half circles of both pulleys (π times the average diameter) and a correction for the pulleys being different sizes: L = 2C + π(D + d)/2 + (D − d)²/4C. Gates' Heavy Duty V-Belt Drive Design Manual prints it with 1.57 for π/2; this calculator uses π.

Use pitch diameters. For a V-belt the pitch line runs through the belt where it carries the load, so the result is the pitch length the catalogue lists (classical V-belts use the datum system). If you measure outside diameters instead, the same formula gives the outside length, which is how Gates lists its 5V belts.

Worked example from Gates: a 5V drive with an 11.8 in driver at 870 rpm, a 46.0 in driven sheave and 41.0 in centers. 2 × 41 + π × 57.8 ÷ 2 + 34.2² ÷ 164 = 82 + 90.79 + 7.13 = 179.92 in. The drive runs 5VX1800 belts, 180 in long.

Center distance from a belt length

Turned round, the formula gives the center distance for a belt you already have or a standard length you want to use. The Center distance tab solves it exactly: with b = L − π(D + d)/2, C = (b + √(b² − 2(D − d)²)) ÷ 4. Gates' manual gets there with a correction factor h read from a table; the answers agree to a fraction of an inch.

No center distance yet? Gates suggests starting at the larger of the big pulley's diameter or half of (D + 3d), working out the belt length, picking the nearest standard belt and then calculating the actual center distance for it. The calculator shows that starting value under every result.

Pulley speed, speed ratio and belt speed

The belt moves both pulleys at the same surface speed, so the rpm scale inversely with the diameters: driven rpm = driver rpm × driver diameter ÷ driven diameter. The speed ratio is the larger diameter over the smaller. A real V-belt slips a little under load, so the driven pulley runs slightly slower than the figure.

Belt speed is the pitch circumference times the rpm: π × d × rpm ÷ 12 in feet per minute with d in inches, or π × d × rpm ÷ 60,000 in meters per second with d in millimeters. Gates' example: 11.7 in pitch diameter at 870 rpm is 2,665 ft/min. Gates limits its sheaves to 6,500 ft/min rim speed; check the limit for your belts and sheaves in the maker's catalogue.

Wrap angle on the small pulley

Each straight span leaves the line of centers at φ = asin((D − d) ÷ 2C), so the belt wraps 180° − 2φ on the small pulley and 180° + 2φ on the large one. Gates' quick approximation is 180° − 60(D − d)/C; in its example drive that gives 129.95° against 130.7° from the exact formula.

The smaller the wrap, the less grip the small pulley has. Gates' manual corrects a drive's rated capacity with an arc of contact factor (Factor K) from its tables, so a big speed ratio on a short center distance needs a check against the catalogue, or more belts.

From the result to the belt you order

The calculator gives a pitch length, not a part number. Belts come in standard lengths that differ by section and maker, and V-belt lengths may be quoted as pitch, datum or outside length, so pick the nearest standard length in that maker's catalogue and set the center distance to suit with the motor base or take-up.

Timing belts are stricter: York Industries notes that a timing belt's length must be a whole multiple of its pitch, so the center distance follows from the tooth count rather than the other way round.

For power transmission reps and maintenance techs

The numbers for a belt drive quote come up on the plant floor: the motor nameplate, the sheave sizes, the belt that keeps failing, how much room is left on the motor base and what the maintenance lead has already tried. Miss one and the replacement drive comes back.

Sources, each read on 2026-10-27. Results are for a two-pulley open belt; the belt maker's catalogue decides the belt:

More for manufacturers' reps and sales engineers: Sales engineer, Manufacturers' rep, Industrial distributor sales, Manufacturing plant tour.

The drive specs come up on the plant walk

The motor nameplate, the sheave sizes and the belt that keeps failing are all said out loud as you walk the line. Record the visit in ParrotNotes and get a transcript, a summary and the action items, so the quote matches what you measured and heard.

Get Started Free

Related tools

Belt length and pulley FAQ