# Pulley Calculator

This pulley calculator developed by us analyzes a physical system of two pulleys joined by a common conveyor belt or any other form of a connective mechanical device. The user can use it to calculate the pulley RPM (revolutions per minute in one reference frame), but also its diameter, and a few properties of the whole system (such as the pulley speed, tension stressed in the belt, or torque of the system).

### Pulley System

A pulley system consists of two pulleys or multiple pulleys (usually of different diameters) and a belt loop to link the pulleys. These belts through which the pulleys are connected for effective functioning are called conveyor belts or mechanical belts. One of the two pulleys is called the driver pulley (this pulley is generally the main pulley with a large diameter, however, this is not so necessary in every case)- it means that transmitting power is applied to it, causing it to rotate in a particular frame of time again and again.

The other pulley is called the driven pulley (this pulley is generally referred to as the secondary pulley with a smaller diameter in comparison to the driver pulley, however, this is not so necessary in every case). It rotates because of the force transmitted through the belt, and hence it is dependent on the per-minute rotation of the driver pulley.

There are two main parameters or the operatives that are associated with each of the pulleys in a pulley system. The first one is the diameter (mathematically it is twice the radius), and the second one is its angular velocity measured in reference with revolutions per minute. And with these two parameters, it can be easy for the user as well as the developer to find any information regarding this pulley system.

### Pulley Formulas

Once you have clearly understood the pulley system of your question, you can start determining various parameters with the pulley calculator we have developed for you using these formulas

#### Diameter and RPM of Each Pulley

For a pulley system that needs the value of both of the above parameters, the product of pulley diameter which is defined as ‘d’, and RPM (Rate per minute) which is defined as ‘n’ is the same for both driver and driven pulley (in most of the cases where pulled do not work independently in a relative system). It means that **d₁ * n₁ = d₂ * n₂** (d₁ is the diameter of driver pulley and d₂ is the diameter of driven pulley and same stands for n₁ and n₂.

The user can use this particular formula to find any of these four values: driver pulley diameter d₁, its angular velocity n₁, driven pulley diameter d₂, or angular velocity n₂.

#### Belt Velocity in a Pulley System

The speed of the belt in a pulley system can be calculated according to the formula **v = π * d₁ * n₁ / 60**, where the angular frequency is expressed in RPM( revolutions per minute) and the belt velocity in meters per second (both are in their standard units).

#### Belt Length in a Pulley System

The length of the belt in a pulley system is directly dependent on the diameters of both pulleys (driver pulley and driven pulley) and the distance between their centers is denoted by ‘D’: **L = (d₁ * π / 2) + (d₂ * π / 2) + 2D + ((d₁ - d₂)² / 4D)**

The user can also reverse this formula to calculate the distance between the pulleys for a known belt length in any pulley system in which both the pulleys (driver pulley and the driven pulley are of comparable sizes).

#### Belt Tension in a Pulley System

The tension in the belt in a pulley system is directly dependent on the belt velocity and the transmitting power which is denoted by P and v stands for the velocity of the pulley: **F = P / v**

Consequently, the user can use the pulley speed calculator to find the power as well - simply input the values of belt tension and velocity.

#### Torque in a Pulley System

The last values that can be found with this pulley calculator are the drive torque (torque of the driver pulley) and the driven torque (of the driven pulley). The user can use the following equation for this calculation **T = P /(2 * π * n / 60)** where the angular velocity which is defined as n of each pulley is expressed in revolutions per minute.

### How does the Pulley Calculator Work?

The pulley calculator that is developed by our team is easy to use and will give you an answer in a fraction of a second and hence saving your time and energy. Our calculator requires the parameters such as diameter of the pulley, rpm(revolution per minute of the pulley), the torque applied by the pulley etc in order to find the other values as tension per unit length in the pulley system, the velocity of the independent or the relative system and the belt length of the system.

For more concepts check out physicscalculatorpro.com to get quick answers by using the free tools available.

### FAQs on Pulley Calculator

**1. How do you determine the RPM of the pulley?**

RPM can be determined by dividing the number of revolutions taken by a pulley in one sixty seconds.

**2. How does belt length affect RPM of the pulley?**

The belt length itself does not affect the RPM of the pulley, if the right thickness of the pulley is taken.

**3. What is defined as pulley ratio?**

Pulley ratio is defined as the ratio of the pulley's pitch diameter by the pitch diameter of the drive pulley.

**4. Does a smaller pulley spin faster?**

Yes the smaller pulley spins faster than the bigger one due to the more availability of power because of the diameter of the pulley.

**5. How can one make a pulley rotate faster?**

One can make a pulley rotate faster by changing the dimension of the pulley that is reducing the diameter of the pulley.