Math CentralQuandaries & Queries


Question from Janet:

I need to calculate the degree (or is it percent?) of incline of my yard as it slopes away from my house. Do I visualize a right angle formed by a level line from the bottom of the slope to the side of the house, and then
compare the line of the slope against the right angle to get the degree? Or is an incline calculated by the measurement of the rise in 100 feet? For instance, if the ground rises 3 feel in a distance of 100 feet, is that a 3%
incline? And if it rises 4 feet in a distance of 25 feet, is that a 16% incline?
Thanks so much.

Hi Janet.

I'm no expert in how to measure yard slopes, but if you can find a way to measure accurately the horizontal distance and the vertical distance, then you can find either the grade (this is expressed as a percentage of vertical distance over horizontal distance, aka. "rise over run") or the slope in degrees.

So for a horizontal distance of 100 units and a vertical distance of 3 units, here's how to calculate it:

Grade: rise / run = 3 / 100 = 3% grade.

Slope: arctan( rise / run) = arctan (0.03) = 1.72 degrees.

Hope this helps,
Stephen La Rocque.

PS: You can infer correctly from this that a 100% incline is one that
is at a 45 degree angle.

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