An inclined plane is one of the oldest machines around — a tilted surface that turns lifting into pushing. This calculator breaks down exactly what happens to an object on a ramp: how gravity splits into two components, how much friction pushes back, and how fast the object accelerates as a result.
How the Inclined Plane Calculator works
Tilting a surface splits an object's weight (mg) into two perpendicular components. One presses into the ramp — this sets the normal force, N = mg·cosθ. The other pulls along the ramp — the down-slope gravity component, mg·sinθ. Friction opposes whichever way the object is trying to move and is proportional to the normal force: f = μN. Subtracting friction from the down-slope pull gives the net force, and dividing by mass gives the acceleration: a = (mg·sinθ − μN) / m.
Inputs and what they mean
Mass (m) is in kilograms — note that mass actually cancels out of the acceleration formula once you expand it, since both the gravity component and the normal force scale with mass. It still matters for the force values shown in newtons. Incline angle (θ) runs from 0° (flat) to just under 90° (vertical), measured from horizontal. Coefficient of friction (μ) is unitless and describes how grippy the object is against the ramp surface — set it to 0 to model a frictionless surface like ice or a well-oiled slide.
Limits and edge cases
This calculator uses the standard Coulomb friction model and a single coefficient of friction rather than separate static and kinetic values — real objects often need slightly more force to start moving than to keep moving. Near the angle of repose, small measurement errors in μ can flip the result between 'slides' and 'stays put,' so treat values close to that boundary as approximate. The model also assumes a rigid object sliding (not rolling) on a straight, uniform ramp with no air resistance.