# Pulley Calculator

Make use of this free Pulley Calculator to find the basic parameters of pulley system easily. Just enter transmitting power, diameters, RPM of pulleys in the input fields and press on the calculate button to get the pulley velocity, belt length, torque and belt tension as output instantly.

**Ex:** 10, 167, 48, 34.5 or 90

### How to Calculate Pulley System Parameters?

Go through the below-provided steps to get help with solving pully speed, RPM, torque, belt length and belt tension manually. You will find a procedure that is quite easy with a detailed explanation.

**Belt Length:**

- Observe the diameters of two pulley and the distance between their centres.
- Multiply each diameter by π and divide the product by 2.
- Add the results and double the distance between the pulley's centres.
- Find the square of the difference of the diameters and divide it by 4 times the distance between centres.
- Add the results in steps 3 & 4 to get the belt length.

**Belt Velocity:**

- Find diameter and RPM of a pulley
- Multiply the diameter and RPM by π
- Divide the result by 60 to get the belt velocity.

**Torque:**

- Find transmitting power and RPM from the question.
- Multiply two times of RPM by π and divide the product by 60.
- Divide the transmitting power by the result in the above step to find torque.

**Belt Tension:**

- Get the transmitting power and belt velocity.
- Divide the transmitting power by the velocity to check the tension.

### Acceleration Formula

A pulley system has two pulleys of different diameters and a belt loop joining those pulleys. Out of the two pulleys, one pulley is the driver pulley which causes rotation with the help of transmitting power, another pulley is the driven pulley and it rotates due to the force transmitted through the belt. Overall pulley is a simple machine. The important parameters of the pulley are diameter, RPM (revolutions per minute) or velocity.

Here, you can check the important formulas to calculate the diameter, RPM of each pulley, belt tension, torque, and belt length.

1. Diameter and RPM of Pulley

The product of the diameter of the speed of one pulley is equal to another pulley.

dΓéü * nΓéü = dΓéé * nΓéé

2. Belt Velocity or RPM

It is the speed of the belt.

V = (π * dΓéü * nΓéü)/60

3. Belt Length

L = (π * dΓéü/2) + (π * dΓéé/2 + 2D + ((dΓéü - dΓéé)²/4D)

Belt Tension

F = P / V

Torque

T = P / (2 * π * n/60)

Where,

dΓéü is the diameter of the driver pulley

dΓéé is the diameter of the driven pulley

nΓéü is the angular velocity of the driver pulley

nΓéé is the angular velocity of the driven pulley

V is the belt velocity

L is the length of the belt

D is the distance between the centres of two pulleys

P is the transmitting power

F is the belt tension

T is the torque

n is the angular velocity of each pulley

**Example**

**Question: A pulley system has 1000 RPM, 1050 RPM and their angular velocities and 0.5 m, 0.3 m as diameters of driver pulley and driven pulley. The transmitting power and distance between their centres are 1500 W and 1 m. Find belt speed, belt length, torque and tension. **

**Solution:**

Given that

Diameter of the driver pulley dΓéü = 0.5 m

Diameter of the driven pulley dΓéé = 0.3 m

Angular velocity of the driver pulley nΓéü = 1000 RPM

Angular velocity of the driven pulley nΓéé = 1050 RPM

Transmitting power P = 1500 W

Distance between the centres of two pulleys D = 1 m

Belt Velocity V = (π * dΓéü * nΓéü)/60

V = (π * 0.5 * 1000)/60

= 1570.79/60

= 26.179

Belt Length L = (π * dΓéü/2) + (π * dΓéé/2 + 2D + ((dΓéü - dΓéé)²/4D)

= (π * 0.5/2) + (π * 0.3/2 + 2(1) + ((0.5 - 0.3)²/4(1))

= 0.785 + 0.471 + 2 + 0.04/4

= 1.256 + 0.01

= 1.266

Tension F = P / V

= 1500/26.179

= 57.29

Torque of driver pulley T = P / (2 * π * nΓéü/60)

= 1500/(2 * π * 1000/60)

= 1500/(2 * π * 1000/60)

= 1500/104.71

= 14.32

Torque of driven pulley T = P / (2 * π * nΓéé/60)

= 1500/(2 * π * 1050/60)

= 1500/109.95

= 13.64

Therefore, belt speed is 26.179 m/s, belt length is 1.266 m tension is 57.29 N, torque is 14.32 Nm, 13.64 Nm.

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### Frequently Asked Question's on Pulley Calculator

**1. What are the types of pulleys?**

The four different types of pulleys are fixed pulley, movable pulley, compound pulley, block and tackle pulley.

**2. Mention the parameters to form a pulley?**

To calculate the force effect on the body attached to the pulley, there is no need of taking the mass of the pulley. When you are applying the law of conservation of energy, then no need to worry about the pulley and rope energy.

**3. Give examples of pulley system.**

Some of the examples of pulley system are along the lines:

Several pulley systems are used in elevators to take it up and bring it down.

Pulley is used in cranes of construction sites to lift and place heavy materials.

These are used in various exercise equipment to function.

**4. What are the formulas to calculate the parameters of a pulley?**

Belt velocity is V = (π * dΓéü * nΓéü)/60

Belt tension is F = P / V

Belt length is L = (π * dΓéü/2) + (π * dΓéé/2 + 2D + ((dΓéü - dΓéé)²/4D)

Torque is T = P / (2 * π * n/60)