Inclined Plane Calculator (Forces, Friction & Acceleration)
By Santaji GadepatilinUpdated October 29, 2026
On a slope, gravity splits into a component pulling the object down the incline and a component pressing it into the surface, which sets the friction. This inclined plane calculator resolves those forces and gives the acceleration of a sliding object and the force needed to push it up at steady speed.
How to use the inclined plane calculator
Enter the mass, the angle of the slope and the coefficient of friction (use 0 for a frictionless slope). You get the gravity component along the slope, the normal force, the friction force, the acceleration of a sliding object and the force needed to push it up the slope at constant speed.
Inclined plane formulas
F∥ = m g sin θ · N = m g cos θ · Ff = μ N
a = g (sin θ − μ cos θ) · Fup = m g (sin θ + μ cos θ)
Example
A 10 kg block on a 30° slope with μ = 0.2:
- F∥ = 10 × 9.807 × 0.5 = 49.03 N
- N = 10 × 9.807 × 0.866 = 84.93 N, friction = 16.99 N
- a = 9.807 × (0.5 − 0.2 × 0.866) = 3.205 m/s² down the slope
- Push up at constant speed = 66.02 N
Acceleration by angle (m/s²)
| Angle | No friction | μ = 0.2 |
|---|---|---|
| 5° | 0.855 | -1.099 |
| 10° | 1.703 | -0.229 |
| 15° | 2.538 | 0.644 |
| 20° | 3.354 | 1.511 |
| 30° | 4.903 | 3.205 |
| 45° | 6.934 | 5.547 |
| 60° | 8.493 | 7.512 |
Negative values mean friction prevents sliding.
Frequently asked questions
What is the acceleration down an inclined plane?
a = g (sin θ − μ cos θ). Without friction it is simply g sin θ — about 4.9 m/s² on a 30° slope.
What does a negative acceleration mean?
Friction is larger than the pull down the slope, so a block at rest will not start sliding (if μ is the static coefficient) and a sliding block slows down.
At what angle will an object start to slide?
When tan θ exceeds the static coefficient of friction — the angle of repose θ = arctan μs. For μs = 0.5 that is about 26.6°.
How much force is needed to push a load up a ramp?
F = m g (sin θ + μ cos θ) at steady speed, ignoring acceleration. A shallower ramp needs less force but a longer distance.