Inclined plane calculator
Calculate the forces on an inclined plane: weight, parallel and normal components, friction, the block's acceleration and the force to push it up the ramp, with or without friction.
How to useForces and acceleration on an inclined plane
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Inclined plane calculator: what it is for
Enter the mass, the incline angle and the static and kinetic friction coefficients. The calculator resolves the weight into components parallel and perpendicular to the ramp, calculates the normal force, maximum static friction and kinetic friction, tells you whether the block slides or stays put and shows the downhill acceleration and the force to push it up at constant speed. A drawing shows the ramp at the given angle.
Calculations run in your browser and treat the block as a point mass.
How to use
- Enter the mass, angle and friction coefficients.
- See whether the block slides.
- Check the forces.
When to use it
- Solving dynamics problems.
- Estimating the effort to push something up a ramp.
- Studying static and kinetic friction.
Frequently asked questions
How is weight resolved on an inclined plane?
Weight W = m·g splits into a component parallel to the ramp, Wx = W·sin θ, which pulls the block down, and a perpendicular component, Wy = W·cos θ, which is balanced by the normal force.
When does the block slide on its own?
When the parallel component beats the maximum static friction, that is, when tan θ > μs. From there, the downhill acceleration is a = g·(sin θ − μk·cos θ), using the kinetic friction coefficient.
What force do I need to go up the ramp?
To move up at constant speed, the force parallel to the ramp must equal Wx + kinetic friction: F = m·g·(sin θ + μk·cos θ).
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.