Inclined Plane Calculator
Forces on a slope with friction: sliding, acceleration, effort.
About this tool
Enter the mass, ramp angle and static and kinetic friction coefficients. The tool shows the weight components, maximum friction, whether the object slides and how fast it accelerates, and the forces to push it up or hold it in place.
Forces on a slope
On a slope at angle θ, an object's weight mg splits into a component mg sin θ along the slope and mg cos θ into it, which is the normal force. Static friction can resist up to μs × the normal force, so the object stays put until tan θ exceeds μs; that slip angle is arctan μs. Once it slides, kinetic friction μk takes over and it accelerates at a = g(sin θ − μk cos θ). Pushing it up at a steady speed takes mg(sin θ + μk cos θ). A 10 kg box on a 30° ramp with μs = 0.4 and μk = 0.3 slides (the slip angle is 21.8°), accelerating at 2.36 m/s²; pushing it up needs 74.5 N, compared with lifting its 98 N weight straight up. A frictionless ramp's mechanical advantage is 1 ÷ sin θ, 2× at 30°: you push with half the force over twice the distance. Honest limits: friction coefficients depend heavily on materials, surface finish and moisture, so use measured values where you can. This models a sliding block, not wheels. The force calculator and the centripetal force calculator are related.
Frequently asked questions
How do I calculate the force down a slope?
Multiply the weight (m × g) by the sine of the slope angle.
When does an object start sliding down a ramp?
When the tangent of the angle exceeds the coefficient of static friction.
What is the mechanical advantage of a ramp?
1 ÷ sin θ without friction. A 30° ramp halves the force needed.
What is the acceleration down an inclined plane?
a = g(sin θ − μk cos θ), or g sin θ without friction.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.