Block and Tackle Calculator

Find Mechanical Advantage, Velocity Ratio, & Efficiency of A Block and Tackle Pulley System

Block and Tackle System Calculator

Block and Tackle System Calculator

Calculate Mechanical Advantage, Velocity Ratio, and Efficiency

Formulas

The following formulas are used in block and tackle systems:

Mechanical Advantage (MA) = Load / Effort
Velocity Ratio (VR) = Number of Pulleys
Efficiency (η) = (MA / VR) × 100%

Where:

  • Load = Output force (weight being lifted)
  • Effort = Input force (applied force)
  • Number of Pulleys = Total pulleys in the system

Calculator

Enter any three values to calculate the fourth:

Results

Mechanical Advantage

–

Ratio of Load to Effort

Velocity Ratio

–

Number of Pulleys

Efficiency

–

Percentage of ideal performance

Example Problem

A block and tackle system has 5 pulleys. If an effort of 1000 N is needed to raise a load of 4500 N, calculate:

(a) Mechanical Advantage: MA = Load / Effort = 4500 N / 1000 N = 4.5

(b) Velocity Ratio: VR = Number of Pulleys = 5

(c) Efficiency: η = (MA / VR) × 100% = (4.5 / 5) × 100% = 90%

How to Find Mechanical Advantage, Velocity Ratio, & Efficiency of a Block and Tackle Pulley System

A block and tackle pulley system is a smart way to lift heavy loads using a combination of ropes and pulleys. By spreading the weight across several ropes, it lets you lift something very heavy with less effort. To understand how well the system works, we often calculate three key things: Mechanical Advantage (MA), Velocity Ratio (VR), and Efficiency (η). Here’s how to find each one.

1. Mechanical Advantage (MA)

Mechanical Advantage tells you how many times the pulley system multiplies your input force.

  • Formula: MA=Load/Effort
  • Meaning:
    • Load is the weight you’re lifting.
    • Effort is the force you apply to the rope.
  • Example:
    If you lift a 100 kg weight with only 25 kg of pulling effort, MA=100/25=4. This means the system makes you four times stronger than pulling the weight directly.

2. Velocity Ratio (VR)

Velocity Ratio shows the relationship between how far you pull the rope and how far the load actually rises.

  • Formula: VR=Distance moved by effort/Distance moved by load ​
  • Shortcut for Block and Tackle:
    In an ideal system (without friction), VR is equal to the number of rope segments supporting the load.
  • Example:
    If there are 4 rope segments holding the bottom block, you must pull 4 m of rope to lift the load 1 m, so VR=4VR = 4VR=4

3. Efficiency (η)

No pulley is perfect because the friction in the wheels and ropes reduces performance.
Efficiency tells you how close the system is to ideal conditions.

Formula: η(%)=(MA/VR)×100

Example:
Suppose your system has MA=3.6 and VR=4

η=3.64×100=90%

This means the system works at 90% efficiency, with 10% lost to friction.

Key Tips for Accurate Calculations

  • Count only the rope segments supporting the load when finding VR.

  • Measure effort and load in the same units (Newtons or kilograms of force).

  • Efficiency will always be less than 100% in real-life setups due to friction.