Real-world applications of slope

Real-world applications of slope, just to mention a few, are the grade of a road, wheelchair ramp for the handicapped, and roof pitch.

What is the grade of this road? Let's see how the slope can be used to find it.

Steep roadSteep road

To represent the grade of a road, numbers like 3%, 5%, 8% and 15% are used. Such a number tells you how steep a road is on a hill or mountain.

Recall that slope  = m = rise / run

Suppose that the rise and the run are measured in feet. Then, a 15% grade means that the road rises 15 feet for every horizontal distance of 100 feet.

Slope = grade of the road = rise / run = 15 / 100 = 15%

A 15% grade is not very steep, but the authorities may decide that this is steep enough to alert drivers. See what a 15% grade looks like on a graph paper.

Grade of the road is 15%

The beautiful road that you see in the image above is very steep. If I could take a guess, I would say that the grade of this road is at least 30%. A 30% grade is very steep!

Question #1

A road has a 6% grade and a vertical run of 2 miles. How high will you travel vertically on that road?

click here to see the solution.

Slope and ramp for the handicapped

According to construction laws, the ramp for the handicapped should never exceed a slope or grade of 8.333%.

8.333% = 8.333 / 100 = (8.333 ÷ 8.333) / (100 ÷ 8.333) = 1 / 12.00048 

Therefore, an 8.3% grade means that for every horizontal run of 12 feet, there should be a vertical rise of 1 foot.

Question #2

A wheelchair ramp has a vertical rise of 4.5 feet for every horizontal run of 50 feet. Was the wheelchair ramp built according to construction laws?


Slope = rise / run = 4.5 / 50 = (4.5 × 2) / 50 × 2 = 9 / 100 = 9%.

Therefore, the slope was not built according to construction laws.

Slope and roof pitch of a house

The roof pitch, also called roof slope, is simply the steepness of the roof of a house. The roof pitch can be found by looking for the number of inches the roof rises vertically for every 12 inches of horizontal run.

Roof pitch

A roof pitch of 3/12 means that the roof rises 3 inches for every 12 inches of horizontal run.

The roof pitch depends on the material, such as asphalt, you put on the roof. One material may require a roof pitch of 3/12 while other materials may a roof pitch that is more or less. 

Other real-world applications of slope

The grade of a treadmill

When a cardiologist is testing how strong your heart is, the cardiologist may decide to change the slope or grade of the treadmill in order to see how it is going to affect your heart rate.

The slope of a windshield

Did you ever notice that the windshield for a car (not a truck!) is not vertical? Car designers must carefully calculate the slope of the windshield for a car so that air drag does not prevent the car from moving smoothly or efficiently. Windshields for fast cars have slopes that are specially low.

The slope of stairs

The slope of stairs should not be too steep since too much effort will be required to use it. The steepness should not be too low either since this may require more space to build the stairs. construction engineers must find the right slope for the stairs.

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