What this calculator does
A belt length calculator works out how long a flat belt or V-belt needs to be to wrap around two pulleys a set distance apart. Enter the diameter of each pulley and the centre distance between their shafts, and the tool returns the belt length using the standard open-belt drive formula, the same calculation used when sizing a replacement belt for a motor, compressor or conveyor.
This matters because a belt cut even a few millimetres short or long either will not seat properly or runs too loose to grip. The formula accounts for the straight sections on either side of the drive plus the curved wrap around each pulley, so it works whether the two pulleys are the same size or very different sizes.
The formula
The belt length is L = 2C + π(D1+D2)/2 + (D1−D2)²/(4C), where C is the centre-to-centre distance between the two pulley shafts and D1, D2 are the pulley diameters. The first term, 2C, is the two straight runs of belt between the pulleys. The second term is the average circumference contribution from both pulleys. The third, smaller term corrects for the extra wrap when the pulleys are different sizes, and disappears entirely when D1 equals D2.
| Term | Meaning |
|---|---|
| C | centre distance, the straight-line gap between the two pulley shaft centres |
| D1, D2 | the diameters of the two pulleys, in any consistent unit |
| L | the calculated belt length, in the same unit as the diameters and centre distance |
| V-belt | a belt with a trapezoidal cross-section that sits in a matching pulley groove, common on motors and compressors |
The inputs explained
| Field | What to enter |
|---|---|
| Centre distance between pulleys (mm) | The straight-line distance between the centres of the two pulley shafts, not the gap between their edges |
| Pulley 1 diameter (mm) | The diameter of the first pulley, measured across the outside edge |
| Pulley 2 diameter (mm) | The diameter of the second pulley, measured the same way |
When to use it
Replacing a worn belt with no size marked on it
Measure the centre distance and both pulley diameters directly off the machine and this calculator gives the belt length to order or cut, without needing the original part number.
Designing a new belt drive
Working out belt length as part of choosing pulley sizes and shaft spacing for a motor-driven pump, fan or conveyor, before parts are bought.
Checking a v belt length calculator result by hand
The same formula applies to V-belts as to flat belts, since it is based on the pulley outside diameters and centre distance rather than the belt cross-section shape.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does belt length change with centre distance?
With both pulleys the same diameter, the belt length grows in step with the centre distance.
| Centre distance (mm) | Belt length |
|---|---|
| 200 mm | 714.2 mm |
| 300 mm | 914.2 mm |
| 400 mm | 1,114.2 mm |
| 500 mm | 1,314.2 mm |
| 600 mm | 1,514.2 mm |
| 800 mm | 1,914.2 mm |
How does belt length change with pulley size difference?
Keeping the large pulley and centre distance fixed, shrinking the second pulley increases the total wrap slightly.
| Second pulley diameter (mm) | Belt length |
|---|---|
| 150 mm | 1,271.2 mm |
| 120 mm | 1,224.7 mm |
| 90 mm | 1,179.2 mm |
| 60 mm | 1,134.9 mm |
| 30 mm | 1,091.7 mm |
Questions
What is the formula for belt length?
L = 2C + π(D1+D2)/2 + (D1−D2)²/(4C), where C is the centre distance between the two pulley shafts and D1, D2 are the pulley diameters. This is the standard formula for an open (non-crossed) belt drive.
How do I measure belt length on an existing drive?
Measure the centre-to-centre distance between the two shafts and the outside diameter of each pulley, then enter those three numbers here. Measuring the old belt directly also works but stretched or worn belts can give a misleading reading.
Does this formula work for V-belts as well as flat belts?
Yes. The formula is based on the pulley outside diameters and centre distance, not the belt cross-section, so it applies equally to V-belts, flat belts and most round belts.
What happens if the two pulleys are the same diameter?
The correction term (D1−D2)²/(4C) becomes zero, so the belt length simplifies to 2C plus the shared pulley circumference term, exactly as in the equal-pulley worked example above.
For the tooth-count side of a gear or sprocket drive rather than a belt drive, see the gear ratio calculator and the pitch diameter calculator.