Inclined plane forces: a block on a ramp has its weight split into a down-slope pull mg sinθ and a perpendicular press mg cosθ, giving a normal force N = mg cosθ and an acceleration a = g(sinθ − μcosθ). This free calculator returns the whole force set from the mass, angle and coefficient of friction, and tells you whether the block slides or is held.
Put a block on a ramp and gravity still pulls straight down, but the surface only lets it respond in two directions: along the slope and into the slope. Splitting the weight W = mg into those two components is the whole game. The part along the slope is mg sinθ — the pull that tries to slide the block down — and the part pressing into the surface is mg cosθ, which sets the normal force N = mg cosθ. Enter the mass, the ramp angle and the coefficient of friction, and the calculator returns every one of these forces at once, plus the acceleration.
Friction opposes motion, and how you treat it depends on whether the block moves. If the slope is gentle enough that tanθ is less than or equal to the coefficient of friction, the block is static: it stays put, and the friction holding it equals the down-slope pull mg sinθ — not μN. Only once the slope is steep enough to overcome friction does the block start sliding, and then the kinetic friction is f = μN and the acceleration follows a = g(sinθ − μcosθ). Getting that static-versus-sliding distinction right is where most ramp problems go wrong; for the friction force itself, see the friction calculator, and for the underlying F = ma step, the Newton's second law calculator. A fuller walkthrough lives in the guide to friction.
The single most useful thing to notice is that the acceleration carries no mass. Because a = g(sinθ − μcosθ) has cancelled the mass out, a feather and a boulder released on the same ramp accelerate identically — the forces differ, the motion does not. Steepening the ramp raises mg sinθ and the acceleration while lowering mg cosθ and the normal force, until at a vertical 90° wall the normal force vanishes and the block is in free fall.
A 5 kg block sits on a frictionless ramp tilted at 30°. Its weight is W = mg = 5 × 9.81 = 49.1 N. The down-slope pull is mg sinθ = 49.1 × sin30° = 24.5 N, and the normal force is N = mg cosθ = 49.1 × cos30° = 42.5 N. With no friction the acceleration is a = g sinθ = 9.81 × 0.5 = 4.91 m/s². Add a coefficient of friction of 0.25 and the acceleration drops to a = 9.81(sin30° − 0.25 cos30°) = 2.78 m/s²; raise it to 0.60 and tanθ = 0.577 is now below μ, so the block stops sliding altogether and is held static.
The inclined plane is one of the classic simple machines and the backbone of countless real designs: wheelchair and loading ramps, road gradients and runaway-truck escape lanes, conveyor inclines, screw threads and wedges, and every physics problem about a box on a slope. Knowing how the weight splits — and when friction holds versus lets go — is the first step in analysing all of them.
Mass is entered in kilograms (or grams or tonnes), the ramp angle in degrees from 0 to 90, and the coefficient of friction is a pure number with no units. Every force — the weight, mg sinθ, mg cosθ, the normal force and the friction — is returned in newtons, and the acceleration in metres per second squared. Gravity is fixed at g = 9.81 m/s².
Because the acceleration on a ramp is a = g(sinθ - μcosθ), which contains no mass term at all. Mass cancels out: a heavier block feels a larger down-slope force but needs proportionally more force to accelerate it, and the two effects exactly balance. Change the mass and every force scales with it, but the acceleration stays the same.
On a ramp the normal force is N = mg cosθ, not mg. Only the component of the weight perpendicular to the surface presses into it, and that component shrinks as the ramp steepens. On flat ground θ = 0 and cosθ = 1, so N = mg; tilt the surface and N falls, reaching zero at a vertical 90° wall.
At 90° the surface is vertical, so cosθ = 0. The normal force N = mg cosθ becomes zero, the friction f = μN also becomes zero, and the acceleration is a = g(sin90° - μ·0) = g. The block is simply in free fall alongside a vertical wall, accelerating at the full 9.81 m/s².
A block held by friction begins to slide when tanθ exceeds the coefficient of friction, so the critical angle is θ = arctan(μ). Below that angle the down-slope pull mg sinθ is smaller than the maximum friction and the block stays static; above it, friction can no longer hold and the block accelerates down the ramp.