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Inclined Plane Calculator

Find the force components on a ramp.

How it is calculated

An object of mass m on a frictionless slope has weight W = m × g with g = 9.80665 m/s². The tool splits this weight into two components using the slope angle θ measured from the horizontal: the force along the slope F∥ = m·g·sin θ and the force pressing into the surface F⊥ = m·g·cos θ. Enter mass in kilograms (it must be above zero) and the angle in degrees; both forces are in newtons. Friction is not included. With friction the force needed to start the slide is reduced by μ × F⊥, where μ is the friction coefficient. At 0° all of the weight presses into the surface, and at 90° all of it pulls along the slope.

Worked example

A 10 kg crate rests on a 30° ramp. Weight: 10 × 9.80665 = 98.0665 N. Parallel component: 98.0665 × sin 30° = 98.0665 × 0.5 = 49.03 N. Normal component: 98.0665 × cos 30° = 98.0665 × 0.8660 = 84.93 N. Together they form a right triangle whose long side is the full weight.

Try this example →

Common mistakes

  • Entering the angle in radians; the tool expects degrees.
  • Measuring the angle from the vertical instead of the horizontal, which swaps sine and cosine.
  • Entering a weight in newtons or pounds in the mass box.
  • Forgetting friction: a real object may stay put even when F∥ is large, because friction opposes the slide.
  • Assuming the normal force equals the weight; on a slope it is only mg·cos θ.

About this calculator

This calculator resolves the weight of a mass resting on a frictionless inclined plane into two components: the force parallel to the slope, F∥ = mg·sinθ (which pulls the object down the ramp), and the force normal (perpendicular) to the surface, F⊥ = mg·cosθ (which the ramp pushes back with, keeping the object on the surface). These two components always sum vectorially back to the full weight, mg, and together they explain why steeper ramps require more force to hold an object in place.

Physics students use this constantly in introductory mechanics for ramp and incline problems, and it underlies practical applications like calculating the force needed to push objects up loading ramps or the load on retaining structures. Enter the mass and incline angle to get both force components.

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