Belt length calculator
Useful when buying a replacement belt or laying out a new drive. Enter both pulley diameters and the centre distance.
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How to use it
- Enter first pulley diameter, second pulley diameter and centre distance.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
φ = arcsin((D₂ − D₁) ÷ 2C). Length = 2C cos φ + π (D₁ + D₂) ÷ 2 + φ (D₂ − D₁). Common approximation: 2C + π (D₁ + D₂) ÷ 2 + (D₂ − D₁)² ÷ 4C. Wrap angle = 180° − 2φ.
Example
Inputs: First pulley diameter = 100 mm, Second pulley diameter = 200 mm, Centre distance = 500 mm. Result: Belt length: 1,476.24 mm; Length by the approximate formula: 1,476.24 mm; Wrap angle on the small pulley: 168.52 °.
Limits and caveats
- Covers an open belt only, not a crossed belt.
- For V belts and timing belts use pitch diameters, then pick the nearest standard length from the catalogue.
Questions about this tool
Why are there two length results?
The first uses the exact geometry of tangents and arcs; the second is the common textbook approximation. They stay close while the centre distance is large compared with the diameter difference.
Why does wrap angle matter?
The smaller the wrap on the small pulley, the less torque the belt can carry and the more likely it is to slip.
How do I measure the centre distance?
Measure from the centre of one pulley shaft to the centre of the other with the belt at its working tension.