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Open Belt Length and Pulley Spacing

Calculate open belt length and pulley spacing with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

belt length = 2.4737394; belt length engineering approx = 2.4737389. Values use the worked example unit selections.

L = π(R+r) + 2(R−r)asin((R−r)/C) + 2√(C²−(R−r)²)

Worked example

Enter these known values and leave the other values blank.

Diameter of the large pulley
0.2 m
Diameter of the small pulley
0.1 m
Pulley center distance
1 m
Belt length
2.4737 m
Belt length
2.4737 m

Assumptions and limitations

  • An open, uncrossed belt wraps two circular pulleys. Center spacing exceeds the sum of radii. The second result is an engineering approximation; belt thickness and stretch are omitted.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

An open, uncrossed belt wraps two circular pulleys. Center spacing exceeds the sum of radii. The second result is an engineering approximation; belt thickness and stretch are omitted.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. Restrict the physical model to non-singular dimensions and stated principal inverse branches; discrete gear/fringe counts are exact integers.

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