# Belt Length Calculator

The length of any belt can be found easily by using the belt length Calculator.

A long time ago pulleys were used to lift buckets of water from well or rivers. But now they are used everywhere in our life e.g., clocks, construction sites, and elevators. This system is used to transmit torque across axles providing mechanical advance.

## Formula of Belt Length Calculator

To find out belt length, you can use the formula listed below:

$Belt - Length = \left( {\left( {{D_L} + {D_S}} \right) \times \left( {\frac{\pi }{2}} \right)} \right) + \left( {{D_L} - {D_S}} \right) \times \arcsin \left( {\frac{{\left( {{D_L} - {D_S}} \right)}}{{2L}}} \right) + 2\sqrt {\left( {{L^2} - 0.25 \times {{\left( {{D_L} - {D_S}} \right)}^2}} \right)}$

Where,

DL = diameter of the large pully

DS = diameter of the small pully

L = distance between pully axles

Note:

### Example

If the large pully diameter is 10m, the small pully diameter is 5m and the distance between their axles is 15m. find the length of the belt.

Given data

DL = 10m
DS = 5m
L = 15m

To Find

Belt length = ?

Solution

To find out belt length, you can use the formula listed below:

$$Belt ~ Length = \left( {\left( {{D_L} + {D_S}} \right) \times \left( {\frac{\pi }{2}} \right)} \right) + \left( {{D_L} - {D_S}} \right) \times \arcsin \left( {\frac{{\left( {{D_L} - {D_S}} \right)}}{{2L}}} \right) + 2\sqrt {\left( {{L^2} - 0.25 \times {{\left( {{D_L} - {D_S}} \right)}^2}} \right)}$$

Putting values in the formula:

$$Belt ~ Length = \left( {\left( {10 + 5} \right) \times \left( {\frac{{3.14}}{2}} \right)} \right) + \left( {10 - 5} \right) \times \arcsin \left( {\frac{{\left( {10 - 5} \right)}}{{2\left( {15} \right)}}} \right) + 2\sqrt {\left( {{{\left( {15} \right)}^2} - 0.25 \times {{\left( {10 - 5} \right)}^2}} \right)}$$

$$Belt ~ Length = \left( {15 \times 1.57} \right) + \left( 5 \right) \times \arcsin \left( {\frac{5}{{30}}} \right) + 2\sqrt {\left( {225 - 0.25 \times {{\left( 5 \right)}^2}} \right)}$$

$$Belt ~ Length = 23.55 + 5 \times \arcsin \left( {0.166} \right) + 2\sqrt {\left( {225 - 0.25 \times 25} \right)}$$

$$Belt ~ Length = 23.55 + 5 \times 0.166 + 2\sqrt {218.75}$$

$$Belt ~ Length = 23.55 + 0.83 + 29.58$$

$$Belt ~ Length = 53.96$$

### How to use the Belt Length Calculator?

The steps to use the belt length calculator are as follows:

Step 1: Enter the Diameter of the large pully in the first required input.

Step 2: Enter the Diameter of the small pully in the second required input.

Step 3: Enter the Center distance of the pully in the third required input.

Step 4: The calculator will automatically display an answer on the screen.

### Calculator use

To find the length of a belt, you can use our belt length calculator. Just enter the diameter of the large pully DL, the diameter of the small pully DS, and the distance between pully axles L in the required input fields, and the length of a belt will be shown to you in the output field. You can also find the distance between objects by using our distance formula calculator.