When designing a belt drive or replacing the belt on an existing drive, three questions need answering: Which pulley diameters give the required speed? What should the belt length be? How many belts, and of which profile? In this guide we explain the basic formulas of belt and pulley calculation, a worked example, V-belt profiles and how to read belt numbers, step by step.
For belt types, tensioning and failures see our what is a belt guide.
Basic Concepts and Symbols
| Symbol | Meaning | Unit |
|---|---|---|
| d | Effective (pitch) diameter of the small (usually driving) pulley | mm |
| D | Effective diameter of the large (driven) pulley | mm |
| n₁, n₂ | Speed of the driving and driven pulleys | rpm |
| i | Speed (transmission) ratio | — |
| C | Centre distance | mm |
| L | Effective (pitch) length of the belt | mm |
| v | Belt speed | m/s |
Important: Calculations use the effective (pitch) diameter where the belt sits in the groove, not the pulley’s outside diameter. Catalogues give the effective diameter of pulleys separately.
1. Speed Ratio and Pulley Diameter
Ignoring slip, belt speed is the same on both pulleys. Therefore:
i = n₁ / n₂ = D / d → n₂ = n₁ × d / D and D = d × n₁ / n₂
Friction V-belts may slip by about 1–2%, so the actual speed is slightly lower than calculated. Where precise speed is needed, timing (toothed) belts are used.
2. Belt Length
For an open (parallel) belt drive, the approximate belt length is:
L ≈ 2C + π(D + d) / 2 + (D − d)² / (4C)
The standard belt length closest to the calculated length is chosen and the centre distance is recalculated.
3. Centre Distance for a Standard Belt
For the selected standard length L, the actual centre distance is:
b = 2L − π(D + d) and C = [ b + √( b² − 8(D − d)² ) ] / 8
Leave adjustment travel on the motor slide base so the centre distance can be shortened and lengthened for fitting and tensioning.
4. Belt Speed and Wrap Angle
v = π × d × n₁ / 60 000 (d in mm, n₁ in rpm → v in m/s)
The wrap angle on the small pulley is approximately: α ≈ 180° − 57.3° × (D − d) / C. As the wrap angle decreases, the power the belt can transmit falls; take care with very large ratios and short centre distances. Belt speed must stay within the limits the manufacturer specifies for the chosen profile.
Worked Example
For a screen drive, let motor speed n₁ = 1480 rpm, motor pulley d = 200 mm, screen pulley D = 500 mm and target centre distance C ≈ 1000 mm:
| Step | Calculation | Result |
|---|---|---|
| Speed ratio | i = 500 / 200 | 2.5 |
| Screen shaft speed | n₂ = 1480 × 200 / 500 | 592 rpm |
| Approximate belt length | 2×1000 + π×700/2 + 300²/(4×1000) | ≈ 3122 mm |
| Standard length | Nearest standard (e.g. SPB 3150) | 3150 mm |
| Actual centre distance | b = 6300 − π×700 ≈ 4101; C = (4101 + √(4101² − 8×300²)) / 8 | ≈ 1014 mm |
| Belt speed | π × 200 × 1480 / 60 000 | ≈ 15.5 m/s |
| Wrap angle | 180° − 57.3 × 300 / 1014 | ≈ 163° |
After these steps, the number of belts is determined from the power to be transmitted.
5. Number of Belts and Profile Selection
The number of belts is calculated from manufacturers’ catalogues using the power to be transmitted, the service factor (higher for shock loads), belt profile, small pulley diameter, speed, wrap angle and belt length correction factors. The general approach:
- Design power = motor power × service factor (a higher factor for shock loads such as crushers),
- Profile selection (SPZ, SPA, SPB, SPC) according to design power and small pulley speed,
- Power one belt can transmit, from the catalogue, for the chosen profile and pulley diameter,
- Number of belts with wrap angle and length corrections (rounded up).
V-Belt Profiles and Pulley Sizes
| Profile | Top Width (approx.) | Height (approx.) | Recommended Min. Pulley Effective Diameter (approx.) |
|---|---|---|---|
| SPZ | 9.7 mm | 8 mm | 63 mm |
| SPA | 12.7 mm | 10 mm | 90 mm |
| SPB | 16.3 mm | 13 mm | 140 mm |
| SPC | 22 mm | 18 mm | 224 mm |
| Z (classical) | 10 mm | 6 mm | 50 mm |
| A (classical) | 13 mm | 8 mm | 75 mm |
| B (classical) | 17 mm | 11 mm | 125 mm |
| C (classical) | 22 mm | 14 mm | 200 mm |
Minimum pulley diameters may vary by manufacturer; using a smaller pulley shortens belt life. Pulley grooves must suit the belt profile and should be checked with groove gauges.
How to Read a Belt Number
- Narrow profiles (e.g. SPB 3150): The letters give the profile and the number usually gives the effective (pitch) length in mm.
- Classical profiles (e.g. B60): The number often gives the inside length in inches (B60 ≈ 60 inches ≈ 1524 mm inside length); the effective length is a few centimetres longer depending on the profile.
- Cogged (raw-edge) belts: An “X” appears next to the profile letter (e.g. XPB, BX).
- Banded belts: The number of belts is written first (e.g. 3/SPB 3150).
Because length designations can differ by standard and manufacturer, state the definition (inside, outside or effective) along with the profile when ordering.
Common Mistakes
- Using the pulley’s outside diameter instead of the effective diameter.
- Going below the minimum pulley diameter.
- Leaving no adjustment travel on the centre distance.
- Using belts from different batches instead of a matched set on multi-belt drives.
- Using a low service factor for shock loads such as crushers.
Frequently Asked Questions
How is belt length calculated?
With L ≈ 2C + π(D + d)/2 + (D − d)²/(4C); then the nearest standard length is chosen.
How does speed change with pulley diameter?
Speeds are inversely proportional to pulley diameters: n₂ = n₁ × d / D. The larger pulley turns more slowly.
How do I measure belt length from an existing belt?
If the number on the belt cannot be read, the inside circumference can be measured and converted to effective length according to the profile; the most accurate method is to calculate from the pulley diameters and centre distance.
Is a timing belt calculation different?
The logic is the same, but timing belts use tooth numbers and pitch and have no slip.
Example: Choosing a Pulley Diameter for a Required Speed
Suppose the gearbox input shaft of a screw washer should turn at 735 rpm instead of 980 rpm, with a motor pulley (d) of 180 mm:
| Step | Calculation | Result |
|---|---|---|
| Required ratio | i = 980 / 735 | ≈ 1.33 |
| Large pulley diameter | D = 180 × 1.33 | ≈ 240 mm |
| Standard pulley | Nearest standard effective diameter | e.g. 236 or 250 mm |
| Actual speed (D = 236 mm) | 980 × 180 / 236 | ≈ 747 rpm |
| Actual speed (D = 250 mm) | 980 × 180 / 250 | ≈ 706 rpm |
Which standard diameter to choose depends on the speed tolerance. When a pulley is changed, belt length and centre distance must be recalculated.
Example Standard Lengths for Narrow V-Belts
Narrow V-belts are made in standard effective length series. For example, some commonly used SPB lengths are 1250, 1400, 1600, 1800, 2000, 2240, 2500, 2800, 3150, 3550, 4000, 4500 and 5000 mm. Intermediate lengths and series for other profiles should be checked in manufacturers’ catalogues.
Field Example
On a vibrating screen with frequent belt breakage, inspection shows that the motor pulley had previously been replaced after a failure with a smaller pulley, which, to keep the screen speed up, was below the recommended minimum diameter for the belt profile. The belts are also not a matched set. When the correctly sized pulley and large pulley are recalculated and a matched set is fitted, the breakages stop.
Glossary
- Effective (pitch) diameter: The diameter at which the belt sits in the pulley groove.
- Speed ratio: The ratio of the two pulley speeds.
- Wrap angle: The angle through which the belt wraps the small pulley.
- Service factor: An allowance added to power for shock and long operating hours.
- Matched set: A set of belts with very close length tolerances.
More Questions
What should the maximum belt speed be?
The manufacturer’s limit for the belt profile and type applies; at very high speeds pulley balance also becomes important.
What should the centre distance be?
In practice a value between the large pulley diameter and the sum of the two pulley diameters is usually chosen; a very short distance reduces the wrap angle, while a very long one increases belt flap.
How do I know if a pulley groove is worn?
Check it with a groove gauge; in a worn groove the belt bottoms out, slips and glazes.
CSP Mühendislik Support
CSP Mühendislik supports the selection and supply of V-belts, banded belts, pulleys and taper lock bushes for crusher, screen and conveyor drives, and drive alignment. See our crusher spare parts page for crusher drive parts and our vibrating screen spare parts page for screens; for bush types see our shaft bushing guide, and for gearbox drives our gearbox calculation guide.
