Belt Length Calculator
The length of belt that joins two pulleys — open or crossed — from their diameters and the center distance, with the wrap angle on the small pulley, the speed ratio, and the center distance that would suit a standard belt length you already have.
A belt around two pulleys is two straight runs plus two arcs.
How the belt length calculator works
A belt around two pulleys is two straight runs plus two arcs. For an open belt the exact length is close to twice the center distance, plus half the sum of the circumferences, plus a correction for the difference in diameters; a crossed belt swaps the sign of that correction. The wrap on the smaller pulley decides how much torque the belt can transmit without slipping — under about 120° it usually needs an idler.
Formula: L_open ≈ 2C + π(D + d)/2 + (D − d)²/(4C); L_crossed ≈ 2C + π(D + d)/2 + (D + d)²/(4C); wrap = 180° − 2 arcsin((D − d)/(2C))
Worked examples
| Inputs | Belt length (mm) | Note |
|---|---|---|
| 300 and 120 mm pulleys, 800 mm apart | 2,269.9 | about 2,270 mm |
| Crossed | 2,314.9 | longer, and both pulleys wrap more |
| A tight center distance | 1,286.7 | a small wrap |
FAQFrequently asked questions
How do I calculate belt length?
Twice the center distance, plus half the circumferences of both pulleys, plus a correction for the diameter difference squared over four times the center distance. It is the standard approximation and is within a millimeter for ordinary drives.
What is wrap angle?
The arc of the pulley the belt touches. Torque capacity grows with it; V-belt drives want at least 120° on the small pulley, flat belts more.
Why does a crossed belt run longer?
Because the two runs cross between the pulleys instead of running parallel, so each is longer, and the belt wraps further round both pulleys.
How do I pick a standard belt?
Compute the length, choose the nearest standard belt, and set the center distance for it with the last row. Most drives include adjustment for tensioning.
Does belt thickness matter?
For V-belts the pitch diameter is a little less than the outside diameter, and the pitch length differs from the outside length by a few millimeters. Use pitch figures from the belt tables for a precize fit.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.