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# How to calculate ramp inclination

Updated July 19, 2017

The inclination, or slope, of a ramp is the angle of the inclined surface of the ramp from its base. A ramp is a simple machine called an inclined plane. The angle of the ramp describes how steep the climb is to the top of the ramp. A high angle requires a smaller length to reach the top of the ramp, while a low angle results in a longer length to reach the top of the ramp. The mechanical advantage is the change in the work equation (work = force x distance) from the use of a machine. In the case of the ramp, increasing the distance results in a reduction in the force needed to change the height of an object (ignoring friction). The mechanical advantage of a ramp is calculated by dividing the length of the slope of the ramp by the height of the ramp (slope length/height). For example, a ramp with a slope 10 metres long that rises 2 metres would have a mechanical advantage of 5 (10 m/2 m = 5). Decreasing the length of the slope to 6 metres requires a steeper angle and reduces the mechanical advantage to 3 (6 m/2 m = 3).

Measure the length of the ramp along its base and the height of the ramp.

Calculate the angle of the inclination by dividing the height of the ramp by the length of the ramp to yield the tangent of the slope. Use the trigonometric function of the calculator to find the inverse tangent (arctangent) of this value. This will give the angle of the slope (inverse tangent (height/length) = angle).

Determine the per cent of inclination by dividing the height of the ramp by the length of the ramp and multiplying by 100 (height/length x 100 = % slope).

#### Tip

The same calculations can be used to calculate the slope of a hill.

#### Things You'll Need

• Pencil
• Paper
• Ruler
• Calculator with trigonometric function