Belt Length Between Two Pulleys
The belt wraps both pulleys and runs straight between them. The widely used approximation adds the two straight runs to the wrapped arcs, plus a correction term for when the diameters differ a lot.
Your numbers
Belt length
124.88cm
Gear ratio
2.5×
Centre distance
40cm
What it means
About 124.88 of belt, with a 2.5:1 ratio — the small pulley turns 2.5 times for each turn of the large one.
Formula
Belt length = 2 × Centre distance + π ÷ 2 × (Pulley A diameter + Pulley B diameter) + (Pulley A diameter − Pulley B diameter) ² ÷ (4 × Centre distance)
Real belts are chosen slightly shorter to leave tensioning travel, and only come in standard lengths.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Pulley A diameter (cm)The diameter of the larger pulley. | 20 | 0 and up |
| Pulley B diameter (cm)The diameter of the smaller pulley. | 8 | 0 and up |
| Centre distance (cm)The distance between the two shaft centres. | 40 | 0.01 and up |
Step by step
Quick reference table
Results when only Pulley A diameter (cm) changes and everything else stays put.
| Pulley A diameter (cm) | Belt length (cm) | Gear ratio (×) | Centre distance (cm) |
|---|---|---|---|
| 10 | 108.3 | 1.25 | 40 |
| 15 | 116.43 | 1.875 | 40 |
| 20 | 124.88 | 2.5 | 40 |
| 30 | 142.72 | 3.75 | 40 |
| 40 | 161.8 | 5 | 40 |
What each result means
| Result | At default values |
|---|---|
| Belt length (cm)The total length of belt wrapping both pulleys. | 124.88 |
| Gear ratio (×)Front chainring teeth divided by rear sprocket teeth. | 2.5 |
| Centre distance (cm)The distance between the two shaft centres. | 40 |
Common mistakes
Real belts are chosen slightly shorter to leave tensioning travel, and only come in standard lengths.
Glossary
- Pulley A diameter
- The diameter of the larger pulley.
- Pulley B diameter
- The diameter of the smaller pulley.
- Centre distance
- The distance between the two shaft centres.
- Belt length
- The total length of belt wrapping both pulleys.
- Gear ratio
- Front chainring teeth divided by rear sprocket teeth.
Frequently asked questions
Q. How is Belt Length Between Two Pulleys calculated?
Belt length = 2 × Centre distance + π ÷ 2 × (Pulley A diameter + Pulley B diameter) + (Pulley A diameter − Pulley B diameter) ² ÷ (4 × Centre distance) — The belt wraps both pulleys and runs straight between them. The widely used approximation adds the two straight runs to the wrapped arcs, plus a correction term for when the diameters differ a lot.
Q. Can you walk through an example?
With Pulley A diameter 20cm, Pulley B diameter 8cm, Centre distance 40cm, the answer is Belt length 124.88cm.
Q. What do I need to enter?
Enter Pulley A diameter, Pulley B diameter, Centre distance. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Pulley A diameter (cm) moves the answer to Pulley A diameter (cm) 10 → Belt length (cm) 108.3 and Pulley A diameter (cm) 40 → Belt length (cm) 161.8. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Real belts are chosen slightly shorter to leave tensioning travel, and only come in standard lengths.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.