Belt Length Calculator

Our team has created a calculator to calculate the length of the belt of any kind. With the CalCon Belt Length Calculator, you can calculate the length of a V-belt, a toothed belt, and some others. Download our Calcon Calculators mobile application, so you can calculate the length of the belt via your mobile device and do various other calculations, such as calculating various quantities in the field of Physics.

In the continuation of this text, read a bit more about the system with two pulleys, the length of the belt, then how to calculate the belt length using our calculator. Also, take a look at another way to determine pulley length and answers to frequently asked questions on this topic.

What are pulley and belt?

The pulley is a wheel for receiving and guiding the belt in a belt drive.

Cylindrical pulleys are most often made of gray cast iron, cast steel, light metals, steel semi-finished products and are used in transmissions with flat belts.

The V-belt pulley is a pulley on the circumference of which one or more trapezoidal grooves are made for guiding the V-belt.

A tension pulley is a pulley that presses the free arm of the belt, which ensures greater tension and increases the circumferential angle.

A toothed pulley is a belt drive pulley with a toothed belt.

A pulley may have a groove or grooves between flanges around its circumference to locate the cable or belt. The drive element of a pulley system can be a rope, cable, belt, or chain.

The belts can be fastened around pulleys of different sizes to the drive shafts to change speed. As with gears, we have a situation where the larger the wheel, the slower the speed.

Belt drives transmit movement from one rotating pulley to another, each held on a shaft. Pulley axles and wheels can be made of any material, while pulley belts are generally made of a flexible and soft material such as rubber. The grooves on the pulleys and belts help them catch and turn. You should know that there are also chain drives.

Two pulley system – belt length

Pulleys were initially used to lift buckets of water from wells, rivers, etc., and their use began long ago, as far back as 250 BC. Pulleys are widely used today; in clockwork, construction sites, elevators, cars, and so on. The belt system transmits torque (or power) over the axles, ensuring mechanical advancement.

Below we will present the equation for calculating the length of the belts.

Belt Length formula

The formula on which our calculator is based takes into account the length between the axles of the pulleys as well as the diameter of the pulleys, and it is necessary to pack it all into the following expression:

BL = (D_1 + D_2) \cdot \frac {\Pi} {2} + (D_1-D_2) \cdot \arcsin {\frac {D_1-D_2}{2 \cdot L}} \\ \;\\+2 \cdot \sqrt {L^2-0,25 \cdot (D_1-D_2)^2}

Where

• D₁ is the diameter of the large pulley;
• D₂ is the diameter of the small pulley;
• L is the distance between the pulley centers;
• BL is the belt length.

The previous equation can be easily derived if we consider the picture above and the basic rules of planimetry and physics.

Meanwhile, it’s essential to keep in mind that the length of the belt will be in the same units as the diameters of the pulley. So, for example, if the smaller and larger pulley diameters are measured in meters, the belt length will also be expressed in meters.

Practical application

Have you ever been on the field or anywhere else and discovered you had a broken or cracked belt? If you take a closer look, you will notice that it is old and worn and that you cannot distinguish a single word on it. You have no idea what the size is, and you need to order a new one as soon as possible to continue working. The solution is a ribbon and a calculator, to find the belt size straightforward way.

Suppose you have the correct belt and pulleys, but you are unsure how much distance between them. There is also an equation for that. The equation is given below.

\frac {b+ \sqrt {b^2-32 \cdot (D_1-D_2)^2}=C} {16}

Whereas

b = 4\cdot L -6,28 \cdot (D_1+D_2)

How to compute like our Belt Length Calculator?

1. First, you need to determine the larger pulley diameter.

Measure the diameter of the larger pulley with a measuring device.

2. Then determine the diameter of the smaller pulley.

Measure the diameter of the smaller pulley using a measuring device.

3. Then measure the distance between the pulleys.

This represents the distance between the center of the pulleys.

4. Finally, calculate the length of the belt.

Using the equation given above, calculate the length of the belt.

For instance:

Let’s find the required length of the belt if we measured that the diameter of the pulleys is 20 and 40 cm, and the distance between their centers should be 1 meter.

So let’s enter the following values in the calculator:

Diameter of the large pulley D_1 = 40 \; cm

Diameter of the small pulley D_2 = 20 \; cm

Pulley center distance L = 1 \; m

It will essentially solve the following expression in the background, now presented with the given values:

BL = (40 + 20) \cdot \frac {\Pi} {2} + (40-20) \cdot \arcsin {\frac {40-20}{2 \cdot 100}} \\ \;\\+2 \cdot \sqrt {100^2-0,25 \cdot (40-20)^2}

The result is BL = 295,5 \; cm = 2,955 \; m

With the CalCon Belt Length Calculator, you can also calculate the distance between the centers of two pulleys for a given belt length.

Using this calculator, you cannot make a mistake in the calculation because it does not allow you to enter values that do not make sense. If you enter values that do not make sense (e.g., enter a larger diameter in the smaller pulley field), the application will report an error and request a new entry.

Below we will give an overview of an even more straightforward calculation, which is certainly applicable.

Approximate formula

There is another formula for calculating the length of the belt, which is popular among engineers. However, this formula represents a simplification: an approximation of the equation given above.

The engineering equation is:

BL = (D_1+D_2) \cdot \frac {\pi} {2} + 2 \cdot L + \frac {(D_1-D_2)^2} {4 \cdot L } 

Where

• D₁ is the diameter of the large pulley;
• D₂ is the diameter of the small pulley;
• L is the distance between the pulley centers;
• BL is the belt length.

The formula gives good results for two pulleys of approximately the same dimensions slightly further apart. The estimate is worse if one pulley is larger than the other or too close to the other. But because such cases are rare in everyday engineering, engineers have used a simplified expression in the past due to the lack of calculators or computers we have today.

Other calculators

On our website, you can search for various other calculators that can help you in everyday life, whether you are interested in something in the field of health, mathematics, or physics. For example, you can check out Free Fall Calculator, Total Body Water Calculator, as well as some math one’s like Natural Log Calculator, etc. Click to see Other section as well.

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