Inclined Plane Calculator
Free calculate force required, friction, mechanical advantage, and work for objects on inclined planes.
Input Parameters
0 = frictionless, typical: 0.1-0.8
Results
Enter values to calculate
What is an Inclined Plane?
An inclined plane (also called a ramp) is a simple machine that allows you to raise or lower objects with less force by spreading the work over a longer distance.
While you need less force to move an object up an inclined plane compared to lifting it vertically, you must apply that force over a longer distance. The work done (force × distance) remains the same, but the force required is reduced.
Inclined planes are everywhere: ramps, roads, stairs, conveyor belts, and even playground slides. They're one of the six classical simple machines and are fundamental in understanding mechanical advantage.
Inclined Plane Formulas
Force (No Friction)
Friction Force
Total Force (With Friction)
Mechanical Advantage
How to Calculate
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1
Convert mass to kilograms
Convert all mass units to kg for consistent calculations.
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2
Convert angle to radians if needed
Most calculators use degrees, but formulas use radians: θ_rad = θ_deg × π/180.
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3
Calculate force components
F = mg sin(θ) for parallel component, F_f = μmg cos(θ) for friction.
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4
Calculate mechanical advantage
MA = 1/sin(θ) for ideal (frictionless) inclined plane.
Practical Examples
Example 1: Frictionless Ramp
A 10 kg object is on a 30° frictionless ramp. What force is needed to move it up?
Solution:
F = m × g × sin(θ) = 10 kg × 9.81 m/s² × sin(30°)
F = 10 × 9.81 × 0.5 = 49.05 N
Force needed = 49.05 N (vs 98.1 N to lift vertically!)
Example 2: With Friction
Same object with μ = 0.2. What is the total force needed?
Solution:
F_parallel = 49.05 N
F_friction = 0.2 × 10 × 9.81 × cos(30°) = 16.99 N
F_total = 49.05 + 16.99 = 66.04 N
Applications
Loading Ramps
Designing ramps for loading docks, vehicles, and accessibility to reduce required force.
Conveyor Belts
Understanding forces and power requirements for inclined conveyor systems in manufacturing.
Road Design
Calculating forces on vehicles on hills, understanding braking requirements, and road safety.
Education
Teaching simple machines, mechanical advantage, and force decomposition in physics.
Frequently Asked Questions
Why is less force needed on an inclined plane?
The force is applied parallel to the ramp, so only the component of weight parallel to the ramp (mg sin θ) must be overcome, not the full weight (mg).
What is mechanical advantage?
Mechanical advantage (MA) is the ratio of output force to input force. For an inclined plane, MA = 1/sin(θ). A 30° ramp has MA = 2, meaning you need half the force.
Does work change on an inclined plane?
No! Work = force × distance. While force decreases, distance increases proportionally. The work to lift an object to height h is always mgh, regardless of path.
How does friction affect the calculation?
Friction opposes motion and depends on the normal force (mg cos θ). Friction force = μ × normal force, adding to the force needed to move the object up.
What angle gives the best mechanical advantage?
Smaller angles give better mechanical advantage (less force needed), but require longer ramps. There's a trade-off between force reduction and distance traveled.