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Calculators · Free

Open-belt geometric length

Calculate a maintenance technician’s belt path and wrap.

01Enter your values

Runs in your browser

Runs offline in your browser. Once the page and required files have loaded, processing needs no internet.

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Example
mm
mm
mm

How it works

Calculate a maintenance technician’s belt path and wrap.

r=d/2; R=D/2; α=asin((R−r)/C); L=2√(C²−(R−r)²)+π(R+r)+2(R−r)α

Runs in your browser

Discovery source

Your data stays yours

Inputs are processed on this page and are never sent to a server.

About this tool

Calculate a maintenance technician’s belt path and wrap.

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Use tool ↑

How to use it

  1. Enter your values

    Small pitch diameter · Large pitch diameter · Shaft centre distance

  2. Calculate / generate

    Calculate a maintenance technician’s belt path and wrap.

  3. Result

    Geometric belt length: 1,476.24308 mm Small-pulley wrap: 168.521659 ° Each straight span: 497.493719 mm

Calculation method

  1. Use pitch diameters and shaft centre distance for two non-overlapping pulleys.
  2. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.
r=d/2; R=D/2; α=asin((R−r)/C); L=2√(C²−(R−r)²)+π(R+r)+2(R−r)α
Example scenario

Open-belt geometric length

Small pitch diameter
100 mm
Large pitch diameter
200 mm
Shaft centre distance
500 mm
Result
Geometric belt length: 1,476.24308 mm
Small-pulley wrap: 168.521659 °
Each straight span: 497.493719 mm

Frequently asked questions

Limits and key assumptions

Not tension, power capacity or a catalog belt size. Open, coplanar, uncrossed belt only, without idlers or stretch. Outside pulley diameter is not necessarily pitch diameter.

Where does my data go?

Calculations run on your device. Form inputs are not sent to a server.

Terms and definitions

Enter your values

Measurement system

The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.

Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.

Small pitch diameter

Use pitch diameters and shaft centre distance for two non-overlapping pulleys.

Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in

Minimum: 0.001 · Maximum: 1000000 mm

Large pitch diameter

Use pitch diameters and shaft centre distance for two non-overlapping pulleys.

Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in

Minimum: 0.001 · Maximum: 1000000 mm

Shaft centre distance

Use pitch diameters and shaft centre distance for two non-overlapping pulleys.

Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in

Minimum: 0.001 · Maximum: 10000000 mm

Result

Result

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Geometric belt length

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Small-pulley wrap

Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Each straight span

Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Value

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Unit

Use pitch diameters and shaft centre distance for two non-overlapping pulleys. Add two common tangent spans and their wrap arcs; the small-pulley wrap is also shown.

Calculated from your entries using the method below.

Common mistakes and quick fixes

Small pitch diameter · Large pitch diameter · Shaft centre distance

Mistake: Changing units and assuming the entered numbers were converted.

Fix: Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.

Limits and key assumptions

Mistake: Treating a result as valid outside the described scope.

Fix: Not tension, power capacity or a catalog belt size. Open, coplanar, uncrossed belt only, without idlers or stretch. Outside pulley diameter is not necessarily pitch diameter.

Limits and key assumptions

  • Not tension, power capacity or a catalog belt size. Open, coplanar, uncrossed belt only, without idlers or stretch. Outside pulley diameter is not necessarily pitch diameter.
  • Displayed results may be rounded; rounding does not add measurement precision.