Inclined Plane Calculator
a = g(sin θ − μ cos θ), with the forces broken out.
Work out Inclined Plane. a = g(sin θ − μ cos θ), with the forces broken out. Free, with no account and nothing to download.
Optional — gives the time to slide down from rest.
Acceleration down the slope
3.2048 m/s²
It slides
a = g(sin θ − μ cos θ). Gravity's pull along the slope rises with angle while the normal force — and therefore friction — falls, so both terms move against you at once as the slope steepens. That is why the transition from gripping to sliding feels so abrupt rather than gradual. Below the angle of repose the acceleration is reported as zero rather than negative, because friction cannot push something back up a hill.
How the Inclined Plane Calculator works
Enter mass, slope angle and friction coefficient for the acceleration and every force involved. Below the angle of repose the acceleration comes back as zero rather than negative, because friction cannot push something uphill.
Also known as: ramp acceleration calculator · block on a slope calculator · friction on an incline calculator · slope physics calculator
Frequently asked questions
How do I calculate acceleration down a ramp?
a = g(sin θ − μ cos θ). Gravity's component along the slope drives it; friction opposes it, and friction depends on the normal force which is mg cos θ.
Why does the mass cancel out?
Because both the driving force and the friction are proportional to mass. A heavy block and a light one slide down the same slope at the same rate, just as they fall at the same rate.
At what angle does it start to slide?
The angle of repose, arctan(μ). Below it friction holds; above it the block accelerates. It depends only on the coefficient, not on mass or size.
Why does a ramp make lifting easier?
It trades distance for force. Raising something up a shallow ramp needs less force than lifting it vertically, but you push it further — the work done is the same either way.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/inclined-plane-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Inclined Plane Calculator"></iframe>
<p style="font:13px/1.5 system-ui,sans-serif;margin:6px 0 0;color:#64748b">Powered by <a href="https://www.thecalclibrary.com/inclined-plane-calculator" style="color:#64748b">Inclined Plane Calculator</a> from The Calc Library</p>The only condition is that the credit line below the frame stays in place. That one line is what pays for the tool being free — it is how anyone else finds it.