V-belt length calculation: get the belt that actually fits.
Order a V-belt one size off and the drive either will not tension or runs slack and slips. Here is the belt length formula, how centre distance and wrap angle tie in, and a worked example you can copy straight onto the drive sheet.
Why V-belt length calculation matters
V-belts are the workhorse of plant power transmission — fans, pumps, compressors, machine tools. The belt length sets the centre distance between pulleys, and the centre distance sets the wrap angle, which decides how much power the drive can actually transmit before it slips. Get the length wrong and you are back to the stores counter, or worse, nursing a belt that squeals and burns out in weeks.
The good news: belt length is pure geometry. Two pulley diameters and a centre distance give you everything.
The V-belt length formula
For an open belt drive (the normal case, both pulleys turning the same way), the pitch length is:
where C = centre distance, D = large pulley pitch diameter, d = small pulley pitch diameter (all same units).
The first term is the two straight runs, the second wraps the belt around both pulleys, and the third corrects for the difference in pulley sizes. Always use pitch (datum) diameters, not the outside diameter you measure with a tape — the belt's load-carrying cords sit on the pitch line.
Wrap angle (arc of contact)
Wrap angle is how far the belt hugs the smaller pulley. It directly limits grip:
Keep θ above about 120°; closer to 180° is better. If the ratio is large and wrap drops too low, increase the centre distance or add an idler. Below 120° you lose so much grip that the belt slips under load no matter how tight you set it.
Solving for centre distance
In practice you usually pick a standard belt first, then back-solve the centre distance the drive needs:
A practical sanity check: a good starting centre distance is between (D + 1.5d) and 3(D + d). Too short and wrap suffers; too long and the belt whips and flutters.
A worked example: pump drive
A motor pulley of pitch diameter d = 120 mm drives a pump pulley D = 280 mm, with a target centre distance C = 500 mm.
- Straight runs: 2C = 2 × 500 = 1000 mm.
- Wrap term: (π/2)(280 + 120) = 1.5708 × 400 = 628.3 mm.
- Correction term: (280 − 120)² / (4 × 500) = 25,600 / 2000 = 12.8 mm.
- Pitch length: L = 1000 + 628.3 + 12.8 = 1641 mm.
- Wrap angle: 180 − 60(160)/500 = 180 − 19.2 = 160.8° — healthy.
You would now pick the nearest standard belt — an SPA 1650 (datum length 1650 mm) is the closest above 1641 mm. Re-solving for C with L = 1650 nudges the centre distance to about 504.5 mm, well within the adjustment range of a normal motor slide rail.
Choosing a standard belt section
| Section | Top width | Typical use |
|---|---|---|
| Z / SPZ | 10 mm | Light fractional drives |
| A / SPA | 13 mm | Pumps, fans up to ~4 kW |
| B / SPB | 17 mm | General industrial, 4–30 kW |
| C / SPC | 22 mm | Heavy drives, compressors |
Wedge (SP) sections carry more power per belt than classical (Z/A/B/C) for the same width, so they are preferred on new designs. Match the section to the calculated power per belt and the small pulley diameter from the manufacturer's selection chart.
Common mistakes
- Using outside diameter instead of pitch diameter. Overstates length and throws off tension.
- Ignoring wrap angle. A correct length with 100° wrap still slips under load.
- No tensioning allowance. Pick a slide-rail range so you can take up belt stretch and fit/remove belts.
- Mixing belt and pulley sections. An A-section belt in a B-section groove rides wrong and wears fast.
If the V-belt drives a pump, size the motor with our pump power calculation; for a gear-reduction stage instead of a belt, see the spur gear calculation guide.
Frequently asked questions
What is the formula for V-belt length?
L = 2C + (π/2)(D + d) + (D − d)² / (4C), using pulley pitch diameters and centre distance C. Round up to the nearest standard belt.
How do I find centre distance from a belt length?
Rearrange the length formula: C = [B + √(B² − 32(D−d)²)]/16 with B = 4L − 6.28(D + d).
What wrap angle is acceptable?
Keep the small-pulley wrap above about 120°; nearer 180° gives the most grip and power capacity.
Pitch length or outside length?
Always design with pitch (datum) length, measured at the belt neutral axis, to match pulley pitch diameters.