A belt length calculator gives the pitch length of an open belt when you know the two pulley diameters and the center distance. Enter the large pulley diameter D, the small pulley diameter d and the center distance C, and the tool returns the belt pitch length L.
Pick millimeters or inches first and keep every entry in that unit. A second tool works the other way round: give it a belt length and it returns the center distance, so you can test a standard length on your pulleys.
Find belt length
Belt pitch length L = 1476.24 mm (about 58.12 in)
Find center distance
Center distance C = 500.00 mm (about 19.69 in)
Key Takeaways
- The tool returns the pitch length of an open belt on two pulleys, in the unit you choose.
- Which diameter to enter depends on the belt family: datum diameters for classical belts, outside diameters for the narrow series.
- A calculated length rarely equals a catalog code, so pick the nearest standard length and recalculate the center distance.
Table of Contents
- How to use the belt length calculator
- V belt length calculation formula
- Belt length calculation examples
- Center distance from belt length
- From calculated length to a standard belt size
- How to measure a V-belt
- FAQ
- About Longyi Rubber Products Factory
How to use the belt length calculator
Enter D, d and C in the same unit. D is the larger pulley, and the calculator rejects a center distance smaller than half the sum of the two diameters because the pulleys would overlap.
The second tool, Find center distance, takes the belt pitch length L and the same two diameters and solves the same formula for C.
Enter the diameter basis that matches the belt family: datum diameters for classical belts and outside diameters for the narrow series (Gates design manual). If you are still working out the section name, read types of V-belts.
V belt length calculation formula
For an open belt on two pulleys, the pitch length is L = 2C + π(D + d)/2 + (D − d)²/(4C). L is the belt pitch length, C is the center distance, D is the large pulley diameter and d is the small pulley diameter. The middle term is the length wrapped around the two pulleys, and the last term corrects for the wrap angle when the diameters differ.
The Gates design manual publishes the same relationship with 1.57 in place of π/2: belt length = 2C + 1.57 (D + d) + (D − d)²/(4C), where C is the actual center distance. It takes outside diameters for the narrow series and datum diameters for classical belts.
With C = 500 mm, D = 200 mm and d = 100 mm, the 1.57 form gives 1476.00 mm, which is 0.24 mm below the 1476.24 mm from π. The calculator uses π.
Belt length calculation examples
| D / d / C | 2C | π(D + d)/2 | (D − d)² / (4C) | Belt length L |
|---|---|---|---|---|
| 200 / 100 / 500 mm | 1000.00 | 471.24 | 5.00 | 1476.24 mm |
| 250 / 125 / 600 mm | 1200.00 | 589.05 | 6.51 | 1795.56 mm |
| 6 / 3 / 15 in | 30.00 | 14.14 | 0.15 | 44.29 in |
All values are computed with the formula above and rounded to two decimals.
- Example 1 uses C = 500 mm, D = 200 mm and d = 100 mm: 2C = 1000.00 mm, π(D + d)/2 = 471.24 mm, and (D − d)²/(4C) = 5.00 mm. The total is 1476.24 mm, which equals 58.12 in.
- Example 2 uses D = 250 mm, d = 125 mm and C = 600 mm, and the length is 1795.56 mm.
- Example 3 uses D = 6 in, d = 3 in and C = 15 in, and the length is 44.29 in, about 1125 mm.
Type the same three sets into the calculator to check it.
Center distance from belt length
Rearranging the same formula gives the shaft spacing. Set b = L − π(D + d)/2, then C = [b + √(b² − 2(D − d)²)]/4. This is algebra on the formula above, not a separate published rule.
Check it with example 1: L = 1476.24 mm gives b = 1005.00 mm, the square-root term is 995.00 mm and C = 500.00 mm.
From calculated length to a standard belt size
Classical A, B and C codes give the inside length; narrow 3V, 5V and 8V codes give the outside length. Belts come in standard lengths, so select the closest standard length to the formula result and calculate the actual center distance for that belt (Gates design manual). Then allow center distance for installation and take-up (Gates design manual).
The length in a code is measured on different bases. A100 is 100 in of inside length and 5V750 is 75.0 in of outside length (Turn2Engineering V-belt size chart). ISO 4184 designates V-belts by datum length Ld, which replaced the former inside length Li (Optibelt technical manual).
For the A section, the pitch length is 1.3 in longer than the inside length in the code, as in A128 and 129.3 in (Gates design manual). A calculated pitch length of 49.3 in therefore points to A48: inside length 48 in (1219 mm), pitch length 49.3 in (1252 mm). Compare that code on the V-belt size chart before you match it to classic V-belts or to industrial belts.
How to measure a V-belt
Start with the cross-section. Take the top width and the height with calipers and compare both readings with the V-belt size chart.
A used belt may no longer match its original length, so measure the pulley diameters and the center distance and let the calculator work out the length.
Ribbed serpentine belts are sized differently; use the serpentine belt size chart for those. This calculator covers an open belt on two pulleys only.
After fitting, set the tension: the belt tension guide covers that step. Send the code or a photo of the belt if the section is still unclear.
FAQ
What is the formula for V-belt length?
For an open belt on two pulleys, L = 2C + π(D + d)/2 + (D − d)²/(4C). A published variant uses 1.57 in place of π/2 (Gates design manual).
How do I calculate belt length from pulley sizes and center distance?
Enter the two diameters and the center distance in one unit, and read the pitch length L in the result box. Use the diameter basis of your belt family: datum diameters for classical belts, outside diameters for the narrow series (Gates design manual).
How do I find center distance if I know the belt length?
Use the second tool. It solves the same formula for C and reports an error when the belt is too short for the pulley sizes.
Why doesn't my calculated belt length match a catalog size?
Catalogs list standard lengths only, and codes state the length on different bases. Take the nearest standard length and recalculate the center distance for it.
Does this belt length calculator work for serpentine or timing belts?
It covers an open belt around two pulleys. Multi-pulley serpentine layouts with idlers, and timing belts sized by tooth count, need their own method.
Sources
Source names appear here only as references. LYBELT is not affiliated with them.
About Longyi Rubber Products Factory
LYBELT is the brand of Longyao County Longyi Rubber Products Factory (General Partnership), based in Longyao County, Xingtai, Hebei, China, and making rubber belts since 1999. The factory holds IATF 16949 and ISO 9001 certification and works from 130+ rubber compounds.
The range covers automotive, industrial, agricultural, ATV/UTV and motorcycle belts. For OEM and ODM orders, belts are made to the customer's part number, drawing or size, with private label and packaging. Email: luxin@lybelt.com.