Belt Length Calculator
Find belt length for a two-pulley drive.
Distance between the two pulley centres.
Results update as you type.
How it works
The belt length is the total length of belt needed to wrap around two pulleys and connect them, and this belt length calculator computes it from the two pulley diameters and the distance between their centres. Getting this length right is essential when ordering or cutting a belt: too short and it will not fit or will overtension the bearings, too long and it slips or needs an idler to take up the slack. This matters across mechanical drives: conveyor systems, machine tools, HVAC blowers, alternators, and countless industrial machines transmit power through belts and pulleys. Replacing a worn belt or designing a new drive both require the correct length, and buying the nearest standard belt size depends on knowing the theoretical figure first. A belt length calculator removes the guesswork and the risk of a costly mismatch. The formula works by tracing the belt's path in three parts: the two straight runs between the pulleys give twice the centre distance, the wrap around each pulley contributes half pi times the summed diameters, and a small correction accounts for the belt angling when the pulleys differ in size. Maintenance engineers, machine builders, and technicians use a belt length calculator to specify replacement belts and design new transmissions accurately.
L = 2C + (π/2)(D1 + D2) + (D1 − D2)² ÷ (4C)
The belt length of an open two-pulley drive has three parts: twice the centre distance for the two straight spans running between the pulleys, half pi times the sum of the diameters for the arcs the belt wraps around each pulley, and a correction term with the squared diameter difference over four times the centre distance that accounts for the belt angling when the pulleys differ in size. Together they trace the full belt path.
Source:Standard mechanical engineering (open belt drive)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter pulley 1 diameter, pulley 2 diameter and centre distance.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Belt length updates instantly as you type — no button to press.
Frequently asked questions
How is belt length calculated for two pulleys?
For an open belt drive, the length equals twice the centre distance plus half pi times the sum of the two pulley diameters plus the squared difference of the diameters divided by four times the centre distance. The first term covers the straight spans, the second the wrap arcs, and the third corrects for unequal pulley sizes. This gives the total path the belt follows around both wheels.
What is the centre distance?
The centre distance is the straight-line distance between the rotational centres of the two pulleys. It sets the length of the two straight belt spans and strongly influences the total belt length. In adjustable drives, the centre distance can often be changed slightly with a tensioner or sliding motor base to take up belt stretch or accommodate a nearby standard belt size.
Does pulley size difference affect the length?
Yes. When the two pulleys have different diameters, the belt angles slightly between them rather than running perfectly parallel, which adds a small amount of length captured by the correction term with the squared diameter difference. For pulleys of similar size this term is tiny, but for a large speed-reduction drive with very different diameters it becomes more significant and should not be ignored.
Why does my belt need to be a standard size?
Belts are manufactured in standard lengths, so the calculated theoretical length is used to select the nearest available belt. A tensioner or adjustable centre distance then takes up the small difference. Choosing the closest standard size that your drive can tension correctly ensures proper grip, avoids slippage, and keeps bearing loads within limits. This calculator gives the target figure to shop from.
Does this formula apply to crossed belts?
No. This formula is for an open belt drive, where both pulleys turn in the same direction and the belt does not cross itself. A crossed belt, which reverses the driven pulley's direction, follows a different equation because the belt wraps a larger arc on each pulley. For crossed configurations, use the dedicated crossed-belt length formula instead of this open-drive one.