How to measure the distance between two pulley axles?

Measure from the center of one axle to the center of the other. If you can't get to the middle of the axles, measure the distance between the outside edges of both axles and add half the diameter of each axle to that measurement.

What is the difference between an open belt and a cross belt?

With an open belt both pulleys turn in the same direction. A crossed belt runs across the two pulleys, causing the driven pulley to turn in the opposite direction. The belt needs to be slightly longer because it is wrapped around each pulley more times.

Does the length of the belt change the speed at which the pulleys turn?

No. The ratio of the transmission is determined by the diameter of the pulleys and not the belt. The length of the belt only serves to ensure a suitable tension for it to work properly with the pulleys and the distance between them.

Is it possible to determine the wheelbase using a belt that is already in place?

Yes. Enter the length of belt and diameters of both pulleys and leave the center distance field blank. A calculation tool will then calculate the distance. This is useful when a belt breaks and positions of both shafts are fixed.

Why is the winding angle of the smaller pulley lower?

In an open belt drive the belt wraps more than half way around the larger pulley while wrapping less than half way around the smaller pulley. If the wrap angle of the smaller pulley falls below about 120 degrees, a friction belt can slip. So it is helpful to increase the size of the smaller pulley or decrease the center distance.

Belt Length Calculator

Pulleys and belt

Belt configuration

Open belt (pulleys spin the same way)

Crossed belt (pulleys spin opposite ways)

Larger pulley diameter

Smaller pulley diameter

Center distance

Belt length

Compare with the engineering approximation

Show the simpler 2C + (pi/2)(D + d) + (D - d)^2 / (4C) estimate next to the exact length.

Enter any three of the two pulley diameters, the center distance, and the belt length. The calculator solves for the one you leave blank.

Please input values into the fields

Belt length breakdown

The belt length calculator tool calculates the required belt length for wrapping around two pulleys. By entering the diameter of each pulley and the distance between the shafts, it will display the belt length. It is also possible to work backwards. If you enter the length of an existing belt as well as any two of the remaining measurements, it can calculate the missing measurement. This is useful if you need to check the center distance or replacement parts dimensions after a belt has broken.

Calculation of length of a belt drive with two pulleys

Imagine you have a belt that is tightened around two pulleys of different sizes. The belt consists of two straight sections that connect the pulleys and an arc section that wraps around each pulley. The sum of these parts makes up the total length of the belt. The larger the pulleys are and the farther apart they are, the longer the belt will be.

For an open belt drive where both pulleys rotate in the same direction, the exact length is as follows:

L = \frac{\pi}{2}\left(D + d\right) + \left(D - d\right)\arcsin\!\left(\frac{D - d}{2C}\right) + 2\sqrt{C^{2} - \left(\frac{D - d}{2}\right)^{2}}

In this case D is the diameter of the larger pulley, d is the diameter of the smaller pulley and C is the distance between the axles. In a crossed belt, the driven pulley rotates in the opposite direction. As the belt wraps longer around each pulley, the minus sign in the formula is replaced by a plus sign.

L = \frac{\pi}{2}\left(D + d\right) + \left(D + d\right)\arcsin\!\left(\frac{D + d}{2C}\right) + 2\sqrt{C^{2} - \left(\frac{D + d}{2}\right)^{2}}

Example calculation

Assume that the diameter of the large pulley is 20 inches, the diameter of the small pulley is 6 inches and the distance between the two axles is 56 inches. If these values are plugged into the open belt formula, the length of the belt will be approximately 153.72 inches. Using the same values expressed in centimeters: if a 30 cm diameter pulley and a 15 cm diameter pulley are 150 cm apart, then the result is about 371 cm or 3.71 m. As long as all measurements use the same unit of measure, it does not matter which unit you choose to use.

A simplified formula

There is a simpler formula that omits the trigonometric functions; for most belt drives this will be accurate enough, especially if the pulleys are similar in size or far apart.

L \approx 2C + \frac{\pi}{2}\left(D + d\right) + \frac{\left(D - d\right)^{2}}{4C}

If the compare option is enabled then this estimated value will be shown by the calculator along with the exact value and their difference. The error only becomes large if one pulley is significantly larger than the other while both are relatively close together in size.

Wrap Angle and its Significance

The calculation tool also indicates how tightly the belt is wrapped around each pulley. This is called wrap angle. In open belt drives, the contact angle of the large pulley is over 180 degrees while that of the small pulley is less. The contact angle affects the holding power. For friction belts like V-belts, a larger wrap comes with more holding power so a belt can slip if the wrap angle of the small pulley falls below about 120 degrees. In crossed belt drives, both pulleys have equal wrap angles and they are greater than in open belt drives. This is one reason why they can carry heavier loads.

Symbols used:

Symbol	Meaning	Example
$D$	Larger pulley diameter	20 in
$d$	Smaller pulley diameter	6 in
$C$	Center distance between axles	56 in
$L$	Belt length	153.72 in

Scope of application:

This calculator can be used when replacing a worn belt, adjusting the distance between two shafts to fit a new drive system or selecting the correct size of pulley for a machine. It supports flat belts, V-belts, round belts and timing belts. The size of the teeth of a timing belt is determined by the belt pitch and cannot be calculated with this tool. Also, it does not calculate the speed or power rating of the belt. To determine these values, you also need to know the RPM of the pulley.

Frequently asked questions

How to measure the distance between two pulley axles?: Measure from the center of one axle to the center of the other. If you can't get to the middle of the axles, measure the distance between the outside edges of both axles and add half the diameter of each axle to that measurement.
What is the difference between an open belt and a cross belt?: With an open belt both pulleys turn in the same direction. A crossed belt runs across the two pulleys, causing the driven pulley to turn in the opposite direction. The belt needs to be slightly longer because it is wrapped around each pulley more times.
Does the length of the belt change the speed at which the pulleys turn?: No. The ratio of the transmission is determined by the diameter of the pulleys and not the belt. The length of the belt only serves to ensure a suitable tension for it to work properly with the pulleys and the distance between them.
Is it possible to determine the wheelbase using a belt that is already in place?: Yes. Enter the length of belt and diameters of both pulleys and leave the center distance field blank. A calculation tool will then calculate the distance. This is useful when a belt breaks and positions of both shafts are fixed.
Why is the winding angle of the smaller pulley lower?: In an open belt drive the belt wraps more than half way around the larger pulley while wrapping less than half way around the smaller pulley. If the wrap angle of the smaller pulley falls below about 120 degrees, a friction belt can slip. So it is helpful to increase the size of the smaller pulley or decrease the center distance.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Belt (mechanical)
Overview of belt drives, belt types, and two-pulley geometry.
Wikipedia: Pulley
Pulley mechanics, angle of wrap, and belt-and-pulley systems.