Quick answer
For two pulleys, belt length L = 2C + π(D + d) ÷ 2 + (D − d)² ÷ (4C), where C is the centre distance. For 10 and 4 inch pulleys 20 inches apart, L = 62.441 inches.
Enter the large and small pulley diameters and the centre distance. The calculator returns the belt length.
Related tools: Rafter Length Calculator: Common rafter length from run and pitch. Length Converter: Convert between metric and imperial lengths. Gutter Length Calculator: Total gutter length and number of sections from your eave lengths.
How to use the Belt Length Calculator
- Enter large pulley diameter (above 0).
- Enter small pulley diameter (above 0).
- Enter center distance (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Large pulley diameter | A number | > 0 |
| Small pulley diameter | A number | > 0 |
| Center distance | A number | > 0 |
Formula and method
Formula
L = 2C + π(D + d) ÷ 2 + (D − d)² ÷ (4C)
IEEE-754 double precision; shown to the decimals indicated.
Standard approximation for an open belt drive; use one length unit throughout. Plan geometry only; confirm quantities with your supplier and local code before ordering.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Large pulley diameter = 10; Small pulley diameter = 4; Center distance = 20.
| Result | Value |
|---|---|
| Belt length | 62.441 |
Example 2
Inputs: Large pulley diameter = 8; Small pulley diameter = 8; Center distance = 15.
| Result | Value |
|---|---|
| Belt length | 55.133 |
Example 3
Inputs: Large pulley diameter = 12; Small pulley diameter = 3; Center distance = 30.
| Result | Value |
|---|---|
| Belt length | 84.237 |
The first line is the headline result (belt length). IEEE-754 double precision; shown to the decimals indicated.
The three parts
2C = 40 inches of straight run, π(D + d) ÷ 2 = 21.99 inches of wrap around the pulleys and (D − d)² ÷ (4C) = 0.45 inches of correction for the belt angle. They sum to 62.44 inches.
Practical use
Round to the nearest standard belt size and allow for tensioner adjustment. The centre distance should exceed the pulley radii. This is for an open belt; crossed belts use a different formula.
How the result changes with large pulley diameter
Holding every other input at the first worked example, this table changes only large pulley diameter. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Large pulley diameter | Belt length |
|---|---|
| 5 | 54.15 |
| 10 | 62.441 |
| 20 | 80.899 |
| 40 | 125.315 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Center distance: entering "0" shows "Center distance must be greater than 0." beside that field and no result.
- Large pulley diameter: entering "0" shows "Large pulley diameter must be greater than 0." beside that field and no result.
Choosing between the Belt Length Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Rafter Length Calculator](/construction/rafter-length/) | horizontal run and pitch | Rafter length |
| [Length Converter](/converters/length-converter/) | value, from and to | Mile (mi) → Kilometre (km) |
| [Gutter Length Calculator](/construction/gutter-length-calculator/) | length of each eave and section length | Total gutter length |
| [Gear Ratio Calculator](/engineering/gear-ratio-calculator/) | driving gear teeth and driven gear teeth | Gear ratio |
| [Spring Constant Calculator](/engineering/spring-constant/) | force and extension | Spring constant |
Background: construction estimates
Material quantities are geometry plus a margin. Calculate the exact volume or area, add an allowance for waste, spillage, cuts and uneven ground (calculator pages commonly mention 5 to 10 percent, a rule of thumb that varies by material and job) and round up to whole units. One cubic yard is exactly 27 cubic feet.
Suppliers often have minimum order sizes and may charge for small loads, so confirm quantities, product yields and local code with your supplier or a qualified estimator before ordering.
Assumptions and limitations
- Center distance should exceed the pulley radii
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for center distance and large pulley diameter to confirm this.
Frequently asked questions
What is the centre distance?
The distance between the shafts.
Does belt thickness matter?
Use pitch diameters for accuracy.
Is it valid for V-belts?
Yes, with pitch diameters.
What does the Belt Length Calculator calculate?
Open-belt length for two pulleys. It returns Belt length.
What formula does the Belt Length Calculator use?
L = 2C + π(D + d) ÷ 2 + (D − d)² ÷ (4C). Standard approximation for an open belt drive; use one length unit throughout.
What do I need to enter in the belt Length Calculator?
You enter Large pulley diameter, Small pulley diameter and Center distance.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Center distance should exceed the pulley radii.
What is an example of a belt Length result?
With large pulley diameter 10, small pulley diameter 4 and center distance 20, the belt length is 62.441.
Where does the method come from?
The method follows: Standard open-belt length approximation (e.g. Shigley's Mechanical Engineering Design).
Can I rely on this calculator for a decision?
Quantities are estimates. Add allowances for waste and site conditions, and follow local codes and a qualified professional's instructions for structural or safety-critical work. For this calculator in particular: Center distance should exceed the pulley radii.
Related calculators
- Rafter Length Calculator — Common rafter length from run and pitch.
- Length Converter — Convert between metric and imperial lengths.
- Gutter Length Calculator — Total gutter length and number of sections from your eave lengths.
- Gear Ratio Calculator — Gear ratio, output speed and torque multiplication.
- Spring Constant Calculator — Hooke's law spring constant and stored energy.
- Transmission Gear Ratio Calculator — Vehicle speed from engine rpm, gear ratio, final drive and tire size.
- Stud Count Calculator — Wall studs from length, spacing, corners and openings.
- Door Rough Opening Calculator — Framing opening size for a door from its slab size.
- Asphalt Tonnage Calculator — Tons of hot-mix asphalt for a paved area.
Sources
- Standard open-belt length approximation (e.g. Shigley's Mechanical Engineering Design)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.