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Work, Energy & Power

Mechanical Advantage Calculator

Calculate mechanical advantage for levers, pulleys, inclined planes, wedges, screws, gears, and wheel & axle systems. Find IMA, AMA, velocity ratio, and efficiency.

Interactive calculator

Mechanical Advantage Calculator

Calculate mechanical advantage for levers, pulleys, inclined planes, wedges, screws, wheels & axles, and gear trains. Find IMA, AMA, and velocity ratio.

Try an example

Force delivered to the load

Force applied by the user

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose a simple machine or calculation type.
  • Enter dimensions, forces, or gear teeth.
  • Click Calculate for IMA, AMA, or gear ratio.

Table of Contents

Key Takeaways

  • Mechanical advantage (MA) = output force / input force.
  • Ideal MA (IMA) ignores friction; actual MA (AMA) accounts for real losses.
  • Six simple machines: lever, pulley, inclined plane, wedge, screw, wheel & axle.
  • MA > 1 multiplies force at the expense of distance or speed.
  • MA < 1 multiplies speed or distance at the expense of force.
  • Energy is always conserved: F_in × d_in = F_out × d_out (ideal).
  • AMA = η × IMA, where η is the machine’s efficiency.

What Is Mechanical Advantage?

Mechanical advantage (MA) is the factor by which a machine multiplies an input force. A lever with MA = 5 means you apply 1 N and the machine delivers 5 N to the load. Every simple machine trades force for distance: you push farther with less force, or push shorter with more force. Energy is conserved—what you gain in force, you lose in distance (or speed).

LeverF_inF_outF_inLoadPulleyhLIncline

IMA vs AMA

IMA=dindoutAMA=FoutFinη=AMAIMAIMA = \frac{d_{in}}{d_{out}} \qquad AMA = \frac{F_{out}}{F_{in}} \qquad \eta = \frac{AMA}{IMA}

Ideal MA (IMA) depends only on geometry—distances, arm lengths, tooth counts. Actual MA (AMA) is measured from real forces and is always less than IMA due to friction. Efficiency η = AMA / IMA.

Lever

IMA=dEdLIMA = \frac{d_E}{d_L}

A lever is a rigid bar pivoting on a fulcrum. Class 1: fulcrum between effort and load (crowbar, seesaw). Class 2: load between fulcrum and effort (wheelbarrow, nutcracker). Class 3: effort between fulcrum and load (fishing rod, tweezers).

Pulley System

IMA=n (supporting ropes)IMA = n \text{ (supporting ropes)}

A single fixed pulley (IMA = 1) only redirects force. A single movable pulley gives IMA = 2. Compound block-and-tackle systems achieve IMA = 4, 6, or more by increasing the number of supporting rope segments.

Inclined Plane

IMA=L/h=1/sin⁡(θ)IMA = L / h = 1 / \sin(\theta)

Ramps reduce the force needed to raise a load by spreading the lift over a longer distance. A 10 m ramp with 2 m rise gives IMA = 5, meaning you need only 1/5 of the load weight as effort (ignoring friction).

Wedge & Screw

textWedge:IMA=L/tqquadtextScrew:IMA=2pir/p\\text{Wedge: } IMA = L/t \\qquad \\text{Screw: } IMA = 2\\pi r / p

A wedge converts a driving force into two spreading forces. A screw is essentially an inclined plane wrapped around a cylinder—each revolution advances the screw by one pitch. Both have very high IMA but significant friction losses.

Wheel, Axle & Gears

textWheel:IMA=R/rqquadtextGears:GR=Ndriven/Ndriver\\text{Wheel: } IMA = R/r \\qquad \\text{Gears: } GR = N_{driven}/N_{driver}

A wheel & axle works like a rotating lever. Gears transmit torque between shafts: a large driven gear on a small driver gear gives torque multiplication (gear-down). Compound gear trains multiply the ratios of each stage.

Typical MA Values

MachineTypical IMATypical η
Crowbar5–1080–90%
Block & tackle (4 ropes)460–75%
Wheelchair ramp (1:12)1250–80%
Wood-splitting wedge4–820–40%
M10 bolt (wrench)300–60010–25%
Car steering system15–2070–85%
Bicycle (high gear)0.3–0.595–98%

How to Use the Calculator

  1. Choose a simple machine type or calculation mode.
  2. Enter the relevant dimensions, forces, or tooth counts.
  3. Click Calculate to see IMA, AMA, gear ratio, or velocity ratio.
  4. Review the formula steps and interpretation.

Example Calculations

Crowbar: 60 cm effort, 10 cm load arm

IMA = 60 / 10 = 6 — the crowbar multiplies force by 6×

Block & tackle with 4 ropes

IMA = 4 — pull with 1/4 the weight, but pull 4× the distance

M10 bolt, 15 cm wrench

IMA = 2π × 0.15 / 0.0015 ≈ 628 — enormous force multiplication

Gear: 48 driver, 16 driven

GR = 16/48 = 0.33 — gear-up: speed ×3, torque ×0.33

Real-World Applications

ApplicationMachine TypePurpose
Automotive transmissionGear trainMatch engine torque to wheel speed
Construction cranePulley systemLift heavy loads with manageable effort
Scissors / shearsClass 1 leverMultiply cutting force at the blade
Wheelchair rampInclined planeReduce force needed to elevate
Bottle jackScrewLift vehicles with small handle force
Bicycle gearsGear trainTrade pedal force for wheel speed

Common Mistakes

  • Confusing IMA (geometric) with AMA (real forces).
  • Assuming a fixed pulley gives mechanical advantage (it only changes direction).
  • Forgetting that friction can reduce AMA to a fraction of IMA (especially screws and wedges).
  • Mixing up gear ratio convention (driver vs driven).
  • Ignoring that MA > 1 trades force for distance—energy is conserved.
  • Using ramp length instead of ramp hypotenuse for incline IMA.

Accuracy and Limitations

IMA calculations assume ideal, frictionless machines. Real machines always have losses from friction, deformation, and wear. AMA must be measured or estimated using efficiency. The calculator does not account for dynamic effects, material limits, or safety factors. This tool is educational and should not replace professional engineering analysis.

FAQ

What is mechanical advantage?›

Mechanical advantage is the ratio of output force to input force. It tells you how much a machine multiplies your effort.

What is the difference between IMA and AMA?›

IMA (ideal mechanical advantage) is calculated from geometry alone, ignoring friction. AMA (actual mechanical advantage) accounts for friction losses and is always less than or equal to IMA.

Can mechanical advantage be less than 1?›

Yes. When MA < 1, the machine trades force for speed or distance. For example, a fishing rod has MA < 1 to amplify the motion at the tip.

Does a fixed pulley give mechanical advantage?›

A single fixed pulley has IMA = 1. It only changes the direction of force, not its magnitude. Movable pulleys and compound systems give IMA > 1.

How do I find the MA of a gear train?›

For a simple pair, MA (torque ratio) = driven teeth / driver teeth. For compound trains, multiply the ratios of each stage.

What is the MA of a screw?›

IMA = 2πr / pitch, where r is the handle radius and pitch is the thread spacing. Screws have very high IMA but also high friction.

Does higher MA always mean better?›

Not necessarily. Higher MA means more force multiplication but slower operation. The best MA depends on the task requirements.

How does friction affect MA?›

Friction reduces AMA below IMA. Efficiency η = AMA / IMA. For screws and wedges, friction can consume over 50% of input work.

Sources

  1. OpenStax University Physics – Simple Machines
  2. HyperPhysics – Simple Machines
  3. MIT OpenCourseWare – Statics
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish