Belt Length Calculator
Calculate the belt length for a two-pulley drive from the pulley diameters and centre distance, for open or crossed belts. Also reports the wrap (contact) angle on each pulley, the speed ratio, and — from a driver speed — the driven pulley speed and belt linear speed. Works in mm, cm or inches.
Input
Applies to both diameters and the centre distance.
Use the pitch diameter where the manufacturer gives one, not the outside diameter.
Shaft-to-shaft distance between the two pulley centres.
Adds the driven (large) pulley speed and the belt's linear speed.
Output
| Quantity | Value | Other units |
|---|---|---|
| No data yet | ||
Guides
Work out how long a belt has to be to wrap two pulleys, from the pulley diameters and the shaft-to-shaft centre distance. The calculator handles both the ordinary open belt and the crossed belt, and adds the numbers that decide whether the drive will actually work: wrap angles, speed ratio and belt speed.
How to use it
- Choose your units — millimetres, centimetres or inches. The same unit applies to both diameters and the centre distance.
- Enter the small pulley diameter (D₁), the large pulley diameter (D₂) and the centre distance (C). If you enter them the other way round the calculator sorts them for you.
- Pick the belt arrangement: open (pulleys turn the same way — nearly always what you want) or crossed (pulleys turn in opposite directions).
- Optionally enter the small pulley speed in rpm to get the driven pulley speed and the belt's linear speed.
Results come back as a table — belt length, wrap angle on each pulley, speed ratio, the free belt span and, if you gave a speed, the driven speed and belt speed — each restated in the other supported units. It downloads as CSV.
The formulas
Open belt:
L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)² / 4C
Crossed belt:
L = 2C + (π/2)(D₁ + D₂) + (D₁ + D₂)² / 4C
Wrap (contact) angles for an open belt are π ∓ 2·asin((D₂ − D₁) / 2C) — smaller on the small pulley, larger on the big one. On a crossed belt both pulleys share the same, larger wrap angle of π + 2·asin((D₁ + D₂) / 2C), which is exactly why a crossed belt grips better but wears faster where the belt rubs against itself.
Pitch diameter or outside diameter?
Use the pitch diameter whenever the manufacturer publishes one. A V-belt rides on its flanks partway down the groove, not on the pulley's outer rim, so the outside diameter overstates the effective diameter and the resulting length will be slightly long.
Why does the wrap angle matter?
Grip depends on how much belt is in contact with the pulley. A wrap angle below roughly 120° on the small pulley means the belt is likely to slip under load — increase the centre distance, use a smaller ratio, or add an idler pulley.
Can I use this result to order a belt?
Treat it as a theoretical length. Belts come in standard pitch lengths, so round up to the nearest stock size and check the manufacturer's table — most drives are designed with adjustable centres or a tensioner precisely so the exact figure doesn't have to be hit.
What if the centre distance is unknown?
The calculator rejects any centre distance smaller than (D₁ + D₂) ÷ 2, because at that point the pulleys physically overlap. If you're designing from scratch, a common rule of thumb is to start at C ≈ D₂ + (D₁ ÷ 2) and adjust from there.
Privacy
The whole calculation runs in your browser. Nothing is uploaded.
Related tools
To find the torque and power the shaft driving that pulley has to carry, use the Shaft Power & Torque Calculator. For chain drives on a bike rather than belts, the Bicycle Gear Ratio Calculator covers chainring/cog ratios and gear inches, and the Bolt Torque Calculator handles tightening the pulley and motor mounts.