Inclined plane calculator

Find the forces on a block on a slope, whether friction holds it, how fast it accelerates and the ramp's mechanical advantage.

By the Calcist team · Checked against known answers · Updated October 27, 2026

Private: calculated on your device. Nothing you type is sent anywhere.

Next: How much power does it take to push it up at a given speed? Use the power calculator with F × v.

What it does

A block on a ramp is the classic physics problem for splitting a force into components. This calculator takes the mass, the angle and (optionally) friction and a push up the slope. It finds every force, decides whether static friction can hold the block, and gives the acceleration. It also shows how hard you'd have to push to move the block up at a steady speed and the ramp's mechanical advantage.

How it's calculated

Gravity pulls straight down with the weight mg, using standard gravity g = 9.80665 m/s². Tilt the axes to line up with the slope and the weight splits into two parts:

Along the slope: F_∥ = mg sin θ · Into the slope: F_⊥ = mg cos θ
Normal force N = mg cos θ
Static friction holds if |F_push − mg sin θ| ≤ μs N
Otherwise a = (|F_push − mg sin θ| − μk N) ÷ m
Ideal mechanical advantage = 1 ÷ sin θ = length ÷ height

Friction always opposes motion (or the tendency to move). If you leave μs empty, the calculator uses μk for both.

Worked example

A 10 kg box sits on a 30° ramp with μk = 0.2 and no push. Weight = 10 × 9.80665 = 98.07 N. Along the slope: 98.07 × sin 30° = 49.03 N. Normal force: 98.07 × cos 30° = 84.93 N. Friction can supply at most 0.2 × 84.93 = 16.99 N, less than 49.03 N, so the box slides. Net force = 49.03 − 16.99 = 32.05 N, and a = 32.05 ÷ 10 = 3.20 m/s² down the slope.

To push it up at a steady speed you'd need 49.03 + 16.99 = 66.02 N. Lifting it straight up takes 98.07 N, so the ramp's actual mechanical advantage is 98.07 ÷ 66.02 = 1.49; without friction it would be 1 ÷ sin 30° = 2.

Angles and ideal mechanical advantage

Angle	sin θ	cos θ	Ideal MA
5°	0.0872	0.9962	11.47
10°	0.1736	0.9848	5.76
15°	0.2588	0.9659	3.86
30°	0.5	0.8660	2
45°	0.7071	0.7071	1.414
60°	0.8660	0.5	1.155

Limitations

The block is treated as a point: no rolling, tipping or air resistance. A rolling ball or wheel accelerates differently because some energy goes into spinning.
Friction coefficients depend on both surfaces and their condition. Measure them if you need a reliable answer.
The push is assumed to be parallel to the slope. A push at another angle also changes the normal force.

Sources

NIST SP 811, Appendix B.9: Conversion factors

How we checked this

Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:

10 kg on 30° with μk 0.2 slides at 3.2048 m/s² ✓
Frictionless 30° slope: g sin θ = 4.9033 m/s² ✓
20° with μs 0.5: static friction holds it ✓
Pushing 100 N up a 30° slope: 3.3981 m/s² up ✓
Flat surface has no mechanical advantage ✓
Angle over 90° is refused ✓

Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.

Add this calculator to your website (free)

Paste this code into any web page. The calculator works on your page, resizes itself, has no ads and no tracking, and nothing your visitors type is sent anywhere. More about embedding.

<iframe src="https://calcist.com/embed/inclined-plane-calculator/" title="Inclined plane calculator" width="100%" height="640" loading="lazy" style="border:0;max-width:760px"></iframe>
<p style="font:14px/1.4 sans-serif;margin:4px 0 0"><a href="https://calcist.com/inclined-plane-calculator/">Inclined plane calculator</a> by Calcist</p>
<script src="https://calcist.com/embed.js" async></script>

Questions people ask

How do you calculate force on an inclined plane?

Split the weight mg into mg sin θ along the slope and mg cos θ into it. The normal force equals mg cos θ, and friction is μ times the normal force.

What is the acceleration down a frictionless incline?

a = g sin θ. On a 30° slope that's 9.80665 × 0.5 = 4.90 m/s².

At what angle does an object start to slide?

When tan θ is greater than the static friction coefficient μs. For μs = 0.5, that's above tan⁻¹(0.5) = 26.6°.

What is the mechanical advantage of an inclined plane?

Ideally, length ÷ height, which equals 1 ÷ sin θ. A 30° ramp halves the force needed, at the cost of moving twice as far.

Does mass affect acceleration on a ramp?

No, not for a sliding block with or without friction: every force scales with m, so a = g(sin θ − μk cos θ) for any mass.

Related calculators

Power calculatorWatts, kW and horsepower from work and time, force and speed, or a circuit.Slope calculatorRise over run, the line's equation, angle and distance.Triangle calculatorSolve any triangle from SSS, SAS, ASA, AAS or SSA, drawn to scale.Speed, distance and timeSolve for speed, distance or time in any units.