Inclined Plane Calculator
An inclined plane, or ramp, lets you raise a heavy load with less force by pushing it over a longer distance. Enter the load weight in newtons, the sloped length of the ramp and the vertical height it rises. The tool returns the ideal mechanical advantage, the frictionless effort force and the incline angle from horizontal.
How to use the inclined plane calculator
- Enter the Load weight in newtons. To convert from mass, multiply kilograms by 9.81.
- Enter the Ramp length, the sloped surface the load travels along, in metres.
- Enter the Ramp height, the vertical rise from bottom to top, in metres.
- Read the mechanical advantage, effort force in newtons and incline angle in degrees.
- Click the copy button to save the three results as a single line.
Examples
Long, shallow loading ramp
weight = 500 N, length = 5 m, height = 1 m
MA = 5, effort = 100 N, angle = 11.536959033 deg
Steeper 30 degree ramp
weight = 500 N, length = 10 m, height = 5 m
MA = 2, effort = 250 N, angle = 30 deg
Wheelchair-style gentle slope
weight = 1000 N, length = 8 m, height = 2 m
MA = 4, effort = 250 N, angle = 14.477512186 deg
Frequently asked questions
What is the mechanical advantage of an inclined plane?
The ideal mechanical advantage is the sloped length divided by the vertical height, MA = length / height. A ramp of 5 metres rising 1 metre gives an advantage of 5, meaning you push with one fifth of the load's weight. Longer and shallower ramps give larger advantages.
How much force does a ramp actually save?
In the frictionless ideal, the effort force is the load weight times the height divided by the slope length, F = W x h / L. So a 500 N load on a 5 metre ramp rising 1 metre needs only 100 N of push. You save force but pay for it by pushing over the longer sloped distance.
How is the ramp angle calculated?
The incline angle from horizontal is the inverse sine of the height over the slope length, angle = asin(h / L), converted to degrees. A ramp of 10 metres rising 5 metres has an angle of asin(0.5) = 30 degrees. The result is rounded to nine decimal places.
Why must the height be no greater than the length?
The height is the vertical rise and the length is the sloped surface, which forms the hypotenuse of the ramp triangle. The hypotenuse is always the longest side, so the height cannot exceed it. Entering a height larger than the length shows an error.
Does this calculation include friction?
No. It models the ideal, frictionless case, so the numbers are a theoretical floor. A real ramp adds friction between the load and surface, so the actual push needed is higher. Smooth rollers or wheels reduce that gap, while rough surfaces widen it.
What units should I use?
Load weight is in newtons, and both ramp length and height are in metres. The mechanical advantage is a pure ratio with no units, the effort force comes out in newtons, and the angle is in degrees. Keep length and height in the same unit so the ratio stays correct.
How do I convert a mass in kilograms to weight in newtons?
Multiply the mass in kilograms by roughly 9.81, the acceleration of gravity on Earth. A 50 kg crate weighs about 490.5 N, which is the value you would enter as the load weight. On other planets the multiplier differs.
Can I use this to check if a ramp is too steep?
Yes. Enter your rise and run and read the angle. Accessibility guidance often caps ramps near a 1 in 12 slope, about 4.76 degrees, so a steeper angle here signals a ramp that may be hard to use or unsafe for a given purpose.
Is my input sent anywhere?
No. The calculation happens locally in your browser, so nothing you type is uploaded, and the tool keeps working offline once the page has loaded.
Learn more
- Inclined plane physics: force, angle and work
How a ramp trades force for distance, why mechanical advantage equals slope over rise, and what changes once friction enters the picture.
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