Belt Length Calculator
Enter the centre distance and the two pulley diameters to get the length of belt needed to wrap an open drive — no crossed belt, just the straight runs plus the wrap around each pulley.
One number, three inputs
Give the centre distance and the large and small pulley diameters and the calculator returns the total belt length in the same unit you entered.
Keep units consistent
Use the same unit for all three inputs — millimetres, inches, whatever — and the result comes back in that unit. Mixing units gives a wrong length.
What does this calculate?
The belt for an open two-pulley drive
The belt length calculator works out how long a belt must be to wrap around two pulleys in an open (non-crossed) drive — the everyday arrangement where both pulleys turn the same way. It takes three measurements, the centre-to-centre distance between the pulley shafts and the diameter of each pulley, and returns the total belt length: the two straight spans plus the arc wrapped over each pulley. It is the number you need before ordering a V-belt or flat belt, sizing a replacement, or laying out a new drive on the bench.
Enter the centre distance and the large and small pulley diameters to get the total belt length instantly, in whatever unit you typed in.
The belt length is the two straight runs between the pulleys (2·C), plus the wrap over both pulleys, which averages out to a half-circle of the combined diameters, plus a small correction for the difference in pulley sizes.
L = 2·C + (π / 2)·(D + d) + (D − d)² / (4·C)Here C is the centre distance, D the large pulley diameter, and d the small pulley diameter. The first term is the two straight spans, the middle term is the average wrap around both pulleys, and the last term corrects for the diameter difference. Because that difference is squared, the order of D and d never matters — swap them and you get the same answer.
Suppose two pulleys sit 300 mm apart, one 120 mm across and the other 80 mm.
Double the centre distance
2 × 300 = 600 mm — the two straight runs of belt between the pulleys.
Add the average wrap
(π / 2) × (120 + 80) = (π / 2) × 200 ≈ 314.16 mm — the belt that hugs both pulleys.
Add the difference correction
(120 − 80)² / (4 × 300) = 1600 / 1200 ≈ 1.33 mm, giving about 915.49 mm of belt in total.
The result is the theoretical length of belt for an open drive — close to what you order in practice, but read it as a starting point rather than a hard cut length. The straight runs (2·C) dominate when the pulleys sit far apart, so the centre distance is the lever that moves the total the most; the wrap term grows with the pulley diameters, and the difference correction is usually tiny — a millimetre or two — and only matters when one pulley is far larger than the other. Standard belts come in fixed lengths, so you normally pick the nearest catalogue size at or just above the figure here, then take up the slack with an adjustable centre distance or an idler. If the two pulleys are the same diameter the difference term vanishes entirely and the belt is simply twice the centre distance plus π times the diameter.
The formula is a clean closed form, but it rests on a couple of assumptions worth keeping in mind.
Open drive and consistent units
This calculator assumes an open (non-crossed) belt, where both pulleys turn the same way — a crossed belt that figure-eights between the pulleys is longer and uses a different formula. It also assumes a thin, inextensible belt and ignores belt thickness, tensioner travel, and groove depth. Keep all three inputs in the same unit; the result comes back in that unit, so mixing millimetres and inches gives a meaningless length.