Two-Pulley Belt Length Calculator
Calculate ideal pitch-line belt length, wrap angles and speed ratio for open or crossed two-pulley routing.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use the exact common-tangent geometry for straight spans and pitch-circle contact arcs. Add both straight spans and both wrap arcs. Apply equal belt speed to obtain the driven pulley speed.
Open: α=asin((R−r)/C), L=2sqrt(C²−(R−r)²)+r(π−2α)+R(π+2α); crossed uses R+r
Worked example
Equal 100 mm pitch diameters at 500 mm center distance have open-belt length 1000+100π≈1314.159 mm. Equal pulleys retain a 1:1 speed ratio.
Assumptions and input details
Pitch diameters, not necessarily outside pulley diameters. Center distance must exceed the sum of radii. Ideal flexible, zero-thickness belt without slip, stretch, sag, pretension, idlers or crossing clearance. Crossed routing is a geometry comparison, not approval for a belt type. No tooth count, standard stock length, load capacity, tension or alignment design is inferred.
References: Gates: pitch-circle belt geometry
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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