How do I use this calculator?

Enter the required values; results and step-by-step derivation update automatically.

Where is Mechanical Advantage used?

Machines and Mechanisms, engineering, research, and related scientific disciplines.

What formulas does this use?

All standard mechanical advantage formulas are applied and shown step-by-step in the results.

Can I get step-by-step solutions?

Yes. The calculator shows a full step-by-step derivation when results are displayed.

How accurate are the results?

Results use standard floating-point arithmetic (~15 significant digits). Suitable for education and professional use.

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MECHANICSMachines and MechanismsPhysics Calculator

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Mechanical Advantage

Mechanical advantage (MA) is the factor by which a simple machine multiplies force. MA = F_out/F_in = d_in/d_out for ideal machines.

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Lever: MA = effort arm / load arm. Pulley: MA equals number of strands supporting load. Ramp: MA = length / height (longer ramp = less force). Screw: MA = 2πr / pitch (finer threads = more MA).

Key quantities

MA = L_effort/L_load

Lever MA

Key relation

MA = number of strands

Pulley MA

Key relation

MA = L/h

Ramp MA

Key relation

MA = 2πr/pitch

Screw MA

Key relation

Ready to run the numbers?

Why: Simple machines reduce effort needed; MA > 1 amplifies force, MA < 1 amplifies distance.

How: Conservation of energy: F_in × d_in = F_out × d_out; MA = d_in/d_out.

Lever: MA = effort arm / load arm.Pulley: MA equals number of strands supporting load.

Sources:Halliday & Resnick - Fundamentals of PhysicsHyperPhysics - Simple Machines

Run the calculator when you are ready.

Solve the EquationCalculate MA for six simple machines

Select Simple Machine

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Lever

🔄

Pulley System

🔩

Screw

🔺

Wedge

📐

Ramp (Inclined Plane)

🎡

Wheel and Axle

⚖️ Lever Parameters

Effort ArmDistance from effort to fulcrum

Load ArmDistance from load to fulcrum

Length UnitUnit for lengths

Force Calculation (Optional)

Input Force (optional)Force applied (for output calc)

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

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Lever MA = effort arm / load arm; fulcrum position determines MA.

— Halliday

🔄

Block and tackle: MA equals strands supporting the load.

— HyperPhysics

📐

Inclined plane: MA = length/height; longer ramp = less force.

— Khan Academy

🔩

Screw MA = 2πr/pitch; finer threads give higher MA.

— NIST

What is Mechanical Advantage?

Mechanical advantage (MA) is the factor by which a simple machine multiplies the input force. It represents the ratio of output force to input force, showing how much easier a machine makes performing work. An MA greater than 1 means the machine amplifies force; less than 1 means it amplifies speed or distance.

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Lever

A rigid bar that rotates around a fixed point (fulcrum)

ext{MA} = ext{Effort} ext{Arm} / ext{Load} ext{Arm}

🔄

Pulley System

Wheels and ropes that redirect and multiply force

ext{MA} = 2 imes ext{Number} ext{of} ext{Pulleys}

🔩

Screw

An inclined plane wrapped around a cylinder

ext{MA} = \text{pi} imes ext{Diameter} / ext{Lead}

How Does Mechanical Advantage Work?

Simple machines don't create energy - they redistribute it. When you gain force, you lose speed or distance, and vice versa. The work done (Force × Distance) remains constant (in an ideal machine), but the machine allows you to apply force more conveniently.

🔬 The Trade-Off Principle

Force Multiplier (MA > 1)

Output force is greater than input force, but input must move farther than output.

Speed Multiplier (MA < 1)

Output moves faster/farther than input, but requires more input force.

When to Use This Calculator

Use this calculator for physics education, engineering design, or whenever you need to understand how simple machines can help accomplish mechanical tasks more efficiently.

🎯 Six Simple Machines

⚖️Lever

🔄Pulley System

🔩Screw

🔺Wedge

📐Ramp (Inclined Plane)

🎡Wheel and Axle

📊 Key Concepts

Work = Force × Distance (constant)

MA = Output Force / Input Force

Velocity Ratio = 1 / MA