Mechanical Advantage Calculator
Free calculate force amplification for pulleys, levers, and gears. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
Ropes directly lifting the load
Results
Enter parameters to calculate
What is Mechanical Advantage?
Mechanical advantage (MA) is a measure of how much a machine amplifies input force. It's the ratio of output force to input force, or input distance to output distance.
MA = Output Force / Input Force = Input Distance / Output Distance. A mechanical advantage greater than 1 means the machine multiplies force (but you move a greater distance). MA < 1 means the machine increases speed/distance but reduces force.
Simple machines like pulleys, levers, and gears provide mechanical advantage. They make work easier by allowing you to apply less force over a greater distance, or more force over a shorter distance.
Mechanical Advantage Formulas
Pulley
MA = Number of supporting ropes
Lever
MA = Effort Arm / Load Arm
Gear
MA = Driven Teeth / Driver Teeth
General
MA = Output Force / Input Force
How to Calculate
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1
Identify the machine type
Determine if it's a pulley, lever, gear, or use force ratio directly.
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2
Apply the appropriate formula
Use MA = ropes (pulley), MA = effort arm/load arm (lever), MA = driven/driver teeth (gear), or MA = output/input force.
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3
Calculate mechanical advantage
Divide the appropriate values to get MA. MA > 1 means force amplification; MA < 1 means speed/distance amplification.
Practical Examples
Example 1: Pulley System
3 supporting ropes lifting the load.
Solution:
MA = Number of supporting ropes = 3
MA = 3 (3× force amplification)
Example 2: Lever
Effort arm: 2 m, Load arm: 0.5 m.
Solution:
MA = 2 / 0.5
MA = 4 (4× force amplification)
Applications
Machinery
Designing mechanical systems, calculating force requirements, and understanding gear ratios in machines.
Lifting Equipment
Designing cranes, hoists, and pulley systems. Understanding how to lift heavy loads with less force.
Transportation
Understanding bicycle gears, vehicle transmissions, and how mechanical advantage affects speed and torque.
Education
Teaching simple machines, understanding work and energy, and demonstrating force amplification principles.
Frequently Asked Questions
What does MA > 1 mean?
MA > 1 means the machine multiplies force - you apply less force but move a greater distance. The work done (force × distance) remains the same (ignoring friction).
Can mechanical advantage be less than 1?
Yes! MA < 1 means the machine increases speed/distance but reduces force. This is useful when you want to move something faster, like in a bicycle's high gear.
Does friction affect mechanical advantage?
Friction reduces the actual mechanical advantage. Ideal MA (theoretical) assumes no friction. Actual MA = Ideal MA × efficiency. Efficiency accounts for friction losses.
How do compound machines work?
Compound machines combine multiple simple machines. Total MA = MA₁ × MA₂ × MA₃... (product of individual mechanical advantages).
What's the difference between MA and velocity ratio?
MA = output force/input force. Velocity ratio = input distance/output distance. For ideal machines (no friction), MA = velocity ratio. With friction, MA < velocity ratio.