Belt Length Calculator

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Open or crossed belt length, angle of contact, belt speed and driven pulley speed from the two pulley diameters and the centre distance

This tool runs entirely in your browser — no file or data is sent to any server.

Enter the values

What to work out

Driver pulley diameter (D₁)

Driven pulley diameter (D₂)

Centre distance (C)

Driver pulley speed (0 to skip)

Result

Belt length

2,952.48mm

Angle of contact on the smaller pulley

168.52°

Belts come in set lengths — take the nearest one from the maker's list and adjust the centre distance.

Working

L = 2C + π(D₁ + D₂) ÷ 2 + (D₂ − D₁)² ÷ (4C)
L = 2 × 1000 + π × 600 ÷ 2 + 200² ÷ (4 × 1000) = 2000 + 942.48 + 10 = 2952.48 mm
α = asin(|D₂ − D₁| ÷ 2C) = asin(200 ÷ 2000) = 5.739°; θ = 180° − 2α = 168.52°
v = π × D₁ × N₁ ÷ 60 = π × 0.2 × 720 ÷ 60 = 7.54 m/s

Formulas

Assumptions

The length formula is the textbook approximate one — very close when the centre distance is large compared with the pulleys.
Belt thickness and slip ignored; worked on the pitch line of a flat belt.

Sources: R. S. Khurmi & J. K. Gupta, Theory of Machines · S. S. Rattan, Theory of Machines

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