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Inclined Plane Calculator

Find acceleration down a ramp plus the parallel, normal and friction forces and the ramp's mechanical advantage.

About this tool

Inclined Plane Calculator is a free, in-browser tool that resolves the forces on a mass resting on a ramp and predicts how fast it accelerates down the slope. Enter the mass, the incline angle and an optional coefficient of friction; the ramp's mechanical advantage as a simple machine is shown too. Everything is computed locally and nothing is uploaded.

Gravity is split into a component along the ramp, m·g·sinθ, and one pressing into it, giving the normal force N = m·g·cosθ (g = 9.81 m/s²). Friction opposes motion with f = μ·N, so the net force down the slope is m·g·sinθ − f and the acceleration is a = g·(sinθ − μ·cosθ). If friction is large enough to cancel the pull, the object does not move and the acceleration is zero. The ramp's ideal mechanical advantage is 1 ÷ sinθ — a gentler slope lets a smaller force raise the same load over a longer distance.

Use it for physics homework, ramp and conveyor design, or to judge whether a load will slide. With μ left at zero you get the classic frictionless result a = g·sinθ.

Frequently asked questions

How is acceleration down a ramp calculated?
The acceleration is a = g·(sinθ − μ·cosθ), the along-ramp gravity component minus friction, divided by mass. Mass cancels out, so acceleration depends only on the angle, the coefficient of friction and g.
Why is the normal force less than the object's weight?
On a slope only the component of weight perpendicular to the surface presses the object against it, so N = m·g·cosθ. The steeper the ramp, the smaller cosθ and the smaller the normal force — reaching zero when vertical.
What is the mechanical advantage of an inclined plane?
As a simple machine the ideal mechanical advantage is 1 ÷ sinθ. A shallow ramp has a high value: you push with less force but over a longer distance to raise a load to the same height.
Is any data uploaded?
No. All force and acceleration math runs in your browser; your inputs never leave your device.

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