About

Incorrect belt sizing causes premature wear, slippage, excessive tension, and drive failure. A belt that is too short overloads bearings. A belt that is too long slips under load and loses transmitted power. This calculator computes the required belt length L for open and crossed belt drives given pulley diameters D and d and center distance C. It also solves the inverse problem: determining the required center distance from a known belt length. Results include the wrap (contact) angle α on the smaller pulley and belt linear speed v. The formulas assume rigid pulleys and inextensible belts. Real belts stretch under load. Add 1 - 2% to the computed length for installation slack on flat belts. For V-belts select the next standard size above the calculated pitch length.

Formulas

Open belt length formula (tangent belt on two pulleys rotating in the same direction):

L = 2C + π2⋅(D + d) + (D − d)²4C

Crossed belt length formula (belt crosses between pulleys, pulleys rotate in opposite directions):

L = 2C + π2⋅(D + d) + (D + d)²4C

Contact (wrap) angle on the smaller pulley for an open belt:

α = 180° − 2 ⋅ arcsin D − d2C

Belt linear speed from driver pulley diameter and rotational speed:

v = π ⋅ D ⋅ n60000

Where: L = belt length mm, C = center distance between pulley shafts mm, D = diameter of larger (driven) pulley mm, d = diameter of smaller (driver) pulley mm, α = wrap angle on smaller pulley °, v = belt linear speed m/s, n = rotational speed of driver pulley RPM.

Reference Data

Belt Cross-Section	Top Width mm	Height mm	Min Pulley ∅ mm	Power Range kW	Speed Limit m/s
Z (SPZ)	10	6	50	0.1 - 3	25
A (SPA)	13	8	75	0.5 - 10	30
B (SPB)	17	11	125	2 - 30	30
C (SPC)	22	14	200	7.5 - 75	30
D	32	19	315	20 - 150	30
E	38	23	500	50 - 300	30
3V (9N)	9.5	8	53	0.3 - 7	50
5V (15N)	15.9	13	180	3 - 50	50
8V (25N)	25.4	23	315	15 - 150	50
Flat (Light)	25 - 50	1 - 3	25	0.05 - 5	40
Flat (Heavy)	50 - 600	3 - 12	100	5 - 500	60
Ribbed PJ	2.34/rib	4	20	0.05 - 2/rib	60
Ribbed PK	3.56/rib	6	45	0.1 - 5/rib	60
Ribbed PL	4.7/rib	10	75	0.5 - 10/rib	60
Ribbed PM	9.4/rib	16.5	180	2 - 30/rib	60
HTD 3M	-	2.4	12	0.01 - 1	40
HTD 5M	-	3.6	27	0.1 - 5	40
HTD 8M	-	6	44	1 - 20	40
HTD 14M	-	10	90	5 - 100	40

Frequently Asked Questions

The contact angle on the smaller pulley should not fall below 120°. Below this value the friction capacity drops significantly and the belt slips under load. The ISO 1081 correction factor for a 120° wrap is approximately 0.83, meaning you lose 17% of rated power. If your calculated angle is below 120°, increase the center distance or reduce the diameter ratio.

Rubber V-belts have a thermal expansion coefficient of roughly 1.5 × 10⁻⁴ per °C. A 1000 mm belt operating at 80 °C above ambient grows about 12 mm. For cold-start environments below −20 °C, belts contract and stiffen, increasing tension on bearings. The calculator assumes ambient temperature. Adjust the result by the thermal coefficient if the operating temperature deviates more than 40 °C from installation temperature.

Use the open belt formula when both pulleys rotate in the same direction (standard configuration for most machinery). Use the crossed belt formula when the driven pulley must rotate in the opposite direction. Crossed belts have higher wrap angles (greater than 180°) which increases friction grip, but they also cause more belt wear due to the self-contact at the crossing point. Crossed belts are uncommon in modern V-belt drives and are mostly used with flat belts.

The formula computes the pitch length - the length measured at the neutral axis (cord line) of the belt, not the outer or inner surface. V-belt manufacturers specify belts by their effective (pitch) length. If you measure around the outside of a belt on pulleys, you get the outer circumference which is longer than pitch length by approximately π times the belt height difference from neutral axis to outer surface. Always compare the calculator output with the manufacturer's pitch length designation.

Geometrically, the center distance must exceed half the sum of both pulley diameters - otherwise the pulleys physically overlap. For practical belt drives, the recommended center distance is between 0.7 × (D + d) and 2 × (D + d). Too short a center distance reduces wrap angle below safe limits and causes belt vibration (flutter). Too long a center distance causes excessive belt sag on the slack side and requires a tensioner idler.

The formulas are geometrically valid for any two-pulley belt system. However, timing belt length must be an integer multiple of the tooth pitch. After computing the theoretical length, divide by the tooth pitch (e.g., 5 mm for HTD-5M), round to the nearest integer, and multiply back. This gives the nearest available synchronous belt length. You then back-calculate the required center distance for that discrete belt length.