Belt Length Calculator
Find the exact length of an open or crossed belt around two pulleys from their diameters and center distance. Or work backwards: enter the belt you have and get the center distance to set the shafts at, along with wrap angles, speed ratio and belt speed.
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Use the pitch diameter for V-belts and timing belts
Pitch length of the belt
How to use the Belt Length Calculator
- Choose what to find: the belt length or the center distance.
- Pick open or crossed belt and your unit.
- Enter both pulley diameters (pitch diameters for V-belts).
- Enter the center distance, or the belt length when solving for the center distance.
- Add the driver RPM if you want speeds, then read the results and the table.
Belt length formulas
| Quantity | Open belt | Crossed belt |
|---|---|---|
| Belt angle φ | asin((D2 − D1) ÷ 2C) | asin((D1 + D2) ÷ 2C) |
| Exact length | 2C·cos φ + π(D1 + D2)/2 + φ(D2 − D1) | 2C·cos φ + (π + 2φ)(D1 + D2)/2 |
| Approximate length | 2C + π(D1 + D2)/2 + (D2 − D1)²/4C | 2C + π(D1 + D2)/2 + (D1 + D2)²/4C |
| Wrap on small pulley | 180° − 2φ | 180° + 2φ |
| Wrap on large pulley | 180° + 2φ | 180° + 2φ |
| Driven speed | N2 = N1 × D1 ÷ D2 | N2 = N1 × D1 ÷ D2 (reversed) |
D2 is the larger pulley in the open-belt formulas, and φ is in radians where it multiplies a length. The approximation is very close when the center distance is several times the difference in diameters.
Worked example
A motor pulley of 3 in drives an 8 in pulley with the shafts 15 in apart. φ = asin(5 ÷ 30) = 9.59°. The exact length is 2 × 15 × cos 9.59° + π × 11 ÷ 2 + 0.1674 × 5 = 29.58 + 17.28 + 0.84 ≈ 47.70 in. The small pulley wrap is 180° − 2 × 9.59° = 160.8°, comfortably above the usual 120° minimum, and the speed ratio is 8 ÷ 3 = 2.67 : 1.
Practical tips
- Round to a stock belt, then use the center distance mode to see where to set the shafts for that belt.
- Allow take-up: plan for adjusting the center distance by a few percent to install and tension the belt.
- Keep the center distance reasonable: for V-belts it is commonly between about the larger pulley diameter and three times the sum of both diameters.
- Need RPM and pulley sizing instead? The Pulley Belt and Speed Calculator focuses on speeds and choosing pulley sizes.
Frequently asked questions
What is the formula for belt length?
For an open belt the exact length is L = 2C·cos φ + π(D1 + D2) ÷ 2 + φ(D2 − D1), where φ = asin((D2 − D1) ÷ 2C) in radians. The widely used approximation is L ≈ 2C + π(D1 + D2) ÷ 2 + (D2 − D1)² ÷ 4C. For 3 in and 8 in pulleys 15 in apart, both give about 47.70 in.
How do I find the center distance for a given belt?
Rearranging the approximate formula gives C ≈ (b + √(b² − 8(D2 − D1)²)) ÷ 8, with b = 2L − π(D1 + D2). This calculator starts from that and then solves the exact formula numerically, so the result fits the belt precisely.
What is the difference between an open and a crossed belt?
In an open belt both pulleys turn the same way. In a crossed belt the belt forms an X between the pulleys, so the driven pulley turns the opposite way and both pulleys get the same, larger wrap angle. Crossed belts are longer and are normally flat or round belts, not V-belts.
What wrap angle is acceptable?
The smaller pulley should usually have at least about 120° of wrap. Below that a V-belt loses grip and may slip. Increasing the center distance or reducing the difference between the pulley sizes increases the wrap.
Which diameter should I use for a V-belt?
Use the pitch diameter, which is where the belt's neutral layer runs, and you get the belt's pitch length. The outside diameter of the pulley is larger. V-belt and timing belt catalogs list belts by pitch length or by a code tied to it.
Why does my belt need adjustment room?
Belts stretch and seat in the grooves as they run in, and they must be slipped over the pulleys during installation. Drives usually allow the center distance to move a little in both directions from the nominal value; the table shows how the length changes with distance.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.