Belt Length Calculator

The Belt Length Calculator works out the length of belt you need to connect two pulleys, using their diameters and the center-to-center distance between their shafts. It supports both open belt and crossed belt drives, returns the exact belt length as well as the familiar textbook approximation, and reports the angle of wrap on each pulley, the speed ratio, and an optional belt speed and driven-pulley RPM. A to-scale diagram of your drive is generated from your actual numbers so you can see the layout at a glance.

How to Calculate Belt Length

The belt has to run in straight tangent lines between the two pulleys and wrap around each one. Adding the straight sections to the wrapped arcs gives the total length. For an open belt, the exact length is:

A widely used approximation, accurate to a fraction of a percent for most drives, assumes the wrap is 180° on both pulleys:

For a crossed belt, where the belt crosses over itself so the driven pulley spins the opposite way, the sign flips in the wrap term and the belt is a little longer:

Here \( D_1, D_2 \) are the pulley diameters, \( R_1, R_2 \) their radii, and \( C \) the center distance. The calculator above handles all the trigonometry for you and shows every step.

Angle of Wrap (Angle of Contact)

The angle of wrap is how much of each pulley the belt actually grips. It controls how much power the belt can transmit before it slips. For an open belt the two wrap angles are:

The smaller pulley always has the smaller wrap angle, so it is usually the one that limits the drive. For a crossed belt both pulleys share the same, larger wrap of \( 180^\circ + 2\alpha \), which is one reason crossed belts can carry slightly more load — at the cost of the belt rubbing against itself where it crosses.

Open Belt vs Crossed Belt

Speed Ratio and Belt Speed

Because the belt does not slip in the ideal case, the two pulleys are linked by their diameters. The speed ratio is simply the ratio of the diameters:

The linear belt speed is the rim speed of the driving pulley, \( v = \pi D_{driver} N_{driver} \). Enter an optional driver RPM in the form to see the belt speed in metres per second and the resulting driven-pulley RPM.

What Affects the Belt Length You Need?

How to Use This Calculator

1. Choose the belt type and units: Pick an open or crossed belt drive and select millimeters, centimeters, or inches.
2. Enter the pulley diameters: Type both diameters in any order — the tool decides which is the larger and smaller pulley for you.
3. Enter the center distance: Add the center-to-center distance between the two shafts.
4. (Optional) Add a driver RPM: Choose which pulley drives and enter its speed to also get belt speed and driven-pulley RPM.
5. Click Calculate: Review the required belt length, the angle of wrap on each pulley, the speed ratio, a to-scale diagram, and a full step-by-step breakdown.

Frequently Asked Questions

How do you calculate the belt length between two pulleys?

For an open belt the length is L = π(R₁ + R₂) + 2α(R₁ − R₂) + 2C·cos(α), where R₁ and R₂ are the pulley radii, C is the center distance, and α = arcsin((R₁ − R₂)/C). A common textbook approximation is L = (π/2)(D₁ + D₂) + 2C + (D₁ − D₂)²/(4C). This calculator gives both values.

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

In an open belt drive both pulleys turn in the same direction and the belt does not cross itself. In a crossed belt drive the belt crosses between the pulleys so the driven pulley turns in the opposite direction. A crossed belt wraps more of each pulley and is slightly longer for the same pulleys and center distance.

What is the angle of wrap and why does it matter?

The angle of wrap (or angle of contact) is the arc of each pulley that the belt grips. A larger wrap angle gives more friction contact, which lets the belt transmit more power before slipping. For an open belt the smaller pulley has the smaller wrap angle, so it usually limits the power the drive can carry.

Does it matter which order I enter the pulley diameters?

No. The calculator automatically treats the larger value as the big pulley and the smaller value as the small pulley, so you can enter the two diameters in any order and still get the correct belt length and wrap angles.

How is belt speed and the driven pulley RPM calculated?

Belt linear speed equals π times the driver pulley diameter times its RPM. The driven pulley speed equals the driver RPM multiplied by the ratio of the driver diameter to the driven diameter. Enter an optional driver RPM and choose which pulley drives to see both values.

Why are the exact and approximate belt lengths slightly different?

The approximate formula assumes the angle of wrap is exactly 180 degrees on both pulleys, which is only true when the pulleys are equal in size. When the diameters differ the exact formula accounts for the true wrap angles, so the two results diverge slightly. For most drives the difference is well under one percent.

Additional Resources

• Belt (mechanical) - Wikipedia
• Pulley - Wikipedia