Belt length for two pulleys.

Worked example

Pulleys of 150 mm and 300 mm diameter with centres 600 mm apart. The exact open-belt formula, L = (d1 + d2) × π ÷ 2 + (d1 − d2) × arcsin((d1 − d2) ÷ 2C) + 2 × √(C² − (d1 − d2)² ÷ 4), gives 706.86 + 18.80 + 1,190.58 = 1,916.24, or 1,916.2 mm. The common approximation, π (d1 + d2) ÷ 2 + 2C + (d1 − d2)² ÷ 4C, gives 1,916.2 mm too. A crossed belt around the same pulleys is 1,992.3 mm.

How it works

An open belt runs around both pulleys on the same side, with two straight runs plus the arcs that wrap each pulley. The exact open-belt formula is L = (d1 + d2) × π ÷ 2 + (d1 − d2) × arcsin((d1 − d2) ÷ 2C) + 2 × √(C² − (d1 − d2)² ÷ 4), where C is the centre distance, and the common approximation is L ≈ π (d1 + d2) ÷ 2 + 2C + (d1 − d2)² ÷ 4C. A crossed belt (the belt twists, reversing the driven pulley) uses L = 2 (r1 + r2) (tan φ + π − φ) with φ = arccos((r1 + r2) ÷ C), written with radii r.

The result is the geometric length at the diameters you enter. For a V-belt that means the pitch diameter, not the outside diameter, and real belts are sold in standard lengths, so the centre distance may need adjusting to fit one. The V-belt centre distance guide (larger than the largest pulley, under three times the sum of both pulleys) is a preferred range, not a limit.

Sources and basis: Belt Length calculator and formula (Redcrab Software); Belt problem (Wikipedia); Belt (mechanical) (Wikipedia). Checked 2026-10-08. Planning and learning aid only. It is not for structural, pressure-system or other safety-critical design, and it is not professional engineering advice. Have a qualified engineer check anything that carries people or could fail dangerously.

FAQ

What is the formula for belt length between two pulleys?

For an open belt, L = (d1 + d2) × π ÷ 2 + (d1 − d2) × arcsin((d1 − d2) ÷ 2C) + 2 × √(C² − (d1 − d2)² ÷ 4), with d the pulley diameters and C the centre distance. The shorter form L ≈ π (d1 + d2) ÷ 2 + 2C + (d1 − d2)² ÷ 4C is close for similar pulleys.

What is the difference between an open and a crossed belt?

An open belt keeps both pulleys turning the same way. A crossed belt twists once between the pulleys and reverses the direction of the driven pulley; it needs a longer belt.

Do I use pitch diameter or outside diameter?

For V-belts and timing belts, belt length is measured at the pitch line, so use pitch diameters. This calculator uses whatever diameters you enter.

What if my belt length is not a standard size?

Choose the nearest standard length and adjust the centre distance to suit, as endless belts come in fixed lengths.

Can I use inches?

Yes. Pick inches; the answer is in the same unit and the other unit is shown beside it.