Math in… Steep Roads

“Iowa Hill Road 15% grade sign” by kittyz202 on Flickr.

On a road trip, you might have noticed a sign like the one on the right. It indicates you’ll be going downhill, and even rates the amount of downhill you’ll be going with a number!

But what does that number mean?

The slope of a line in the plane is its rise over run.

To find this number, take a segment of the line and, reading from the left endpoint to right endpoint, divide the number of units it moves up by the number of units it moves right. (If it moves down instead of up, count those units as negative.)

In the graphic on the left, the top line has a slope of -3/7.

The bottom line has a slope of 1/5.

It doesn’t matter which endpoints you choose for your segment to do the calculation — the number you get will always be the same!

The grade of a road is its slope given as a percentage, and a percentage is just a fraction given as its numerator with an assumed denominator of 100.

“Midway point of Kingsbury Grade descent” by kittyz202 on Flickr.

“Verkehrsschild "14% Gefälle" (zwischen Ziegendorf und Bachmühle)” by AlexanderRahm on Wikimedia Commons.

Knowing the grade of a road helps the government choose reasonable speed limits and helps people driving semi trucks and other vehicles that take a while to slow down anticipate their braking needs.

What’s the steepest road you’ve seen? What do you think its grade is?