Examples
Examples
Try the starting example
- First pulley pitch diameter (mm)
- 100
- Second pulley pitch diameter (mm)
- 100
- Pulley centre distance (mm)
- 500
- Belt configuration: open or crossed
- open
- Ideal pitch-line belt length (mm)
- 1,314.159265
- Small pulley wrap (degrees)
- 180
- Large pulley wrap (degrees)
- 180
Try another scenario
- First pulley pitch diameter (mm)
- 100
- Second pulley pitch diameter (mm)
- 100
- Pulley centre distance (mm)
- 200
- Belt configuration: open or crossed
- crossed
- Ideal pitch-line belt length (mm)
- 765.289182
- Small pulley wrap (degrees)
- 240
- Large pulley wrap (degrees)
- 240
Calculation method
Calculation method
Ideal pitch-line belt length (mm)
Open: two external tangent spans plus the two contact arcs. Crossed: two internal tangent spans plus the two equal wrap arcs. Radii are half the pitch diameters.
Small pulley wrap (degrees)
Open: 180 − 2 × asin((large radius−small radius)/centre distance). Crossed: 180 + 2 × asin((large radius+small radius)/centre distance).
Large pulley wrap (degrees)
Open: 180 + 2 × asin((large radius−small radius)/centre distance). Crossed: same wrap as the small pulley.
Symbols and units
- a
- First pulley pitch diameter (mm)
- b
- Second pulley pitch diameter (mm)
- c
- Pulley centre distance (mm)
- d
- Belt configuration: open or crossed
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Ideal thin flexible belt at supplied pitch diameters, using tangent-and-arc geometry. Does not round to commercial belt sizes or account for belt elasticity, tooth pitch, tensioners or transmission loads.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
OpenStax: arithmetic and geometry ↗
Background reading; this does not imply endorsement or independent review of SumFizz.