Math CentralQuandaries & Queries


Subject: percent gained while hiking
Name: Susan
Who are you: Other

okay... so if I hike Gregory Canyon and it's a 1.1 mile hike with a 900 foot elevation gain, what's the percent elevation gain? I've forgotten my geometry! I do know that 1.1 mile is 5808 feet.
I'm guessing it's a formula utilizing a right triangle? I've searched on the internet but am unable to figure out. Getting old here.

The reason I ask is that it's really cold outside & my favorite hiking trails are covered with much snow. If you show me how to calculate the percentage, I can replicate on the treadmill.
And that way I'll be ready as soon as it warms up and the darn snow melts!

Thanks so much!

Hi Susan.

You are right that it is a right triangle. The hypotenuse is the trail (5808 feet), the height is 900 and so the base is found using pythagorus' theorem. So:

base = sqrt(5808^2 - 900^2) = 5738 feet

Put another way, you have a 900 foot "rise" and a 5738 foot "run". The percentage incline is normally the "gradient" that department of transportation people use. That's expressed as a percentage but is calculated as the rise over the run.

In your case, this is 900/5738 = 15.7 %.
That's fairly steep - it sounds like good exercise!

Hope this helps your training,
Stephen La Rocque.

PS: When it warms up and you get onto it, we'd love to have you email us a photo of the trail ! :)

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