Inclined Plane Calculator
Enter the load weight, the ramp's sloped length and its vertical height to size a frictionless ramp. The tool returns the mechanical advantage, the effort force needed to push the load up and the incline angle.
How to use the inclined plane calculator
- Enter the weight of the load you are moving up the ramp, in newtons.
- Enter the sloped length of the ramp and the height it rises.
- Read the mechanical advantage, effort force and incline angle.
Examples
Long, shallow ramp
weight = 500 N, length = 5 m, height = 1 m
MA = 5, effort = 100 N, angle = 11.54 deg
Steeper ramp
weight = 500 N, length = 10 m, height = 5 m
MA = 2, effort = 250 N, angle = 30 deg
Frequently asked questions
What is the mechanical advantage of an inclined plane?
The ideal mechanical advantage is the sloped length divided by the height, MA = length / height. A longer, shallower ramp gives a larger advantage.
How much force does a ramp save?
Without friction, the effort force is the load weight times the height divided by the slope length. The ramp trades a smaller force for pushing over a longer distance.
How do I find the ramp angle?
The incline angle from horizontal is the inverse sine of the height divided by the slope length, angle = asin(height / length), reported in degrees.
Why must the height be at most the length?
The height is the vertical rise and the length is the sloped surface, which is the hypotenuse. The hypotenuse is always the longest side, so the height cannot exceed it.
Does this include friction?
No. This is the ideal, frictionless case. A real ramp needs a bit more effort to overcome friction, so the actual force is slightly higher.
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