Belt length calculator
Approximate open-belt length from centre distance and pulley pitch diameters.
Fill in the fields and the result will appear here automatically.
An open belt runs around two pulleys without crossing. This calculator estimates its pitch-path length from the diameters and centre distance, then shows the smaller pulley’s wrap angle and the larger-to-smaller diameter ratio. The length formula is an approximation: it is exact for equal pulleys and differs more from exact tangent geometry as the diameter difference becomes large relative to the centre distance. Use it to compare layouts; a numerical length alone does not select a belt or its tension.
How it works
Formula and logic
L ≈ 2C + π(D₁+D₂)/2 + (D₂−D₁)²/(4C), with every input in mm. Wrap α = 180° − 2·arcsin(|D₂−D₁|/(2C))·180°/π. Equal diameters D give L = 2C + πD and 180° wrap. This tool requires C > (D₁+D₂)/2 so the pulleys neither touch nor overlap. That clearance condition is stricter than tangent existence, C > |D₂−D₁|/2.
Example
For C = 300 mm and diameters of 100 and 200 mm, the approximate length is 1079.57 mm and the smaller pulley’s wrap is 160.81°. Exact ideal tangent geometry would give 1079.59 mm. Equal 150 mm diameters at C = 500 mm give 1471.24 mm with either formula.
Fields and units
- Centre distance — mm
- Pitch diameter of first pulley — mm
- Pitch diameter of second pulley — mm
How to use
- — Enter a positive centre distance and two pitch diameters in millimetres.
- — Diameter order does not change the length; the smaller diameter is selected for the wrap angle.
- — Check clearance: C must exceed half the sum of the diameters.
- — Compare the estimate with the selected belt’s catalogue, adjustment travel and manufacturer requirements.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- Optibelt, §2.5: approximate timing-belt pitch length OpenStax: sine and tangent in a right triangle
- Limitation
- Approximate length of an open two-pulley drive without idlers or crossing. Belt thickness, stretch, tension, slip and rated power are not modelled.
FAQ
Why the correction for unequal diameters?
Unequal diameters change both tangent angles and wrapped arc lengths. The term (D₂−D₁)²/(4C) approximates their combined contribution; it is not the exact straight-run length. It vanishes for equal diameters.
Why is a small wrap angle a problem?
Less wrap affects frictional grip or the number of teeth in mesh, but 120° is not a universal limit for every belt. Load capacity and any idler requirement depend on the drive type and manufacturer data.
What if no standard length matches?
Choose a catalogue size compatible with the permitted centre-distance adjustment and tension. The nearest workable size may be shorter or longer than the estimate; always rounding up is not a general rule.
Does this work for a toothed belt?
Pitch diameters can be used to estimate the path geometry. A timing belt’s length is an integer number of pitches; tooth count, teeth in mesh and load rating must be checked against the specific system’s catalogue.