Pulley & Belt Length Calculator
Speed ratio, belt length, centre distance and belt speed from pulley diameters
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Calculates the speed ratio, driven speed and belt speed from two pulley diameters and the driving speed, the belt length from the centre distance, and the centre distance from a belt length. Use it to lay out a belt drive or choose a replacement belt.
How to use
- Choose the "Length unit" and the "Belt arrangement" ("Open belt" or "Crossed belt").
- Enter "Driving pulley diameter", "Driven pulley diameter", "Driving pulley speed" and "Centre distance" to see the driven speed, belt length and wrap angle with a sketch.
- To get the centre distance for a belt you have, enter its length under "Centre distance from belt length".
- Use "Pulley size for a wanted speed" to size a pulley, and "Multi-step drive" for several pairs.
How it works
- Driven speed = driving speed × driving diameter ÷ driven diameter, and belt speed = π × driving diameter × driving speed.
- Belt length uses the exact sum of straight spans and wrapped arcs; the short approximate formula is shown too. The centre distance from a length is solved exactly by iteration.
- Use pitch diameters for V-belts and timing belts. Slip and belt thickness are ignored, and belt section, tension and power rating are not calculated.
Questions and answers
- How do I calculate pulley rpm?
- Multiply the driving speed by the driving diameter ÷ driven diameter. A 100 mm pulley at 1,450 rpm driving a 250 mm pulley gives 1,450 × 100 ÷ 250 = 580 rpm.
- How do I calculate belt length?
- For an open belt, the short formula is 2C + π(D + d) ÷ 2 + (D − d)² ÷ 4C. For 100 mm and 250 mm pulleys at a 500 mm centre distance, the length is about 1,561 mm.
- What pulley size gives the speed I want?
- Required driven diameter = driving diameter × driving speed ÷ wanted speed. From a 120 mm pulley at 1,450 rpm, 700 rpm needs about 248.6 mm.
- What is the difference between an open and a crossed belt?
- With an open belt both pulleys turn the same way; a crossed belt is twisted into an X and the pulleys turn in opposite directions. At the same centre distance a crossed belt is longer and wraps more of each pulley.