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How do you calculate % grades?(7 posts)

How do you calculate % grades?aeon
Jul 15, 2002 8:19 PM
I could never figure out what a percent grade meant. I could do degrees I suppose, given a measure of vertical gain and distance along the road, but % has me stumped.

Of course, I have neither a bike computer nor altimiter, but it might be usefull to know later on...
re: How do you calculate % grades?Leisure
Jul 15, 2002 9:01 PM
Vertical (rise) divided by horizontal (run) x100. Note that horizontal is not the same as the total distance traveled as you would read on your computer. You can also convert grade from degrees by taking the tangent and multiplying that by 100. Don't bother doing it with your eyes while actually climbing the hill, I've tried that and it doesn't work.
re: How do you calculate % grades?aeon
Jul 15, 2002 9:15 PM
Ok thanks. Yeah I know that the distance measured is the hypotenuse, so not a problem.
re: How do you calculate % grades?Birddog
Jul 15, 2002 9:14 PM
The % of a grade is computed by figuring the amount of "rise" (elevation) in the "run" (distance). For instance a 5% grade is equivalent to a 5 foot rise in every 100 feet, an 8% grade would be an 8 foot rise in every 100 feet. In the real world it is a little different. Lets say there is a stretch of road that is 4 miles or 21,120 feet long with an elevation gain of 1,000 feet. You must use the Pythagorean theorem to now calculate the %grade. You know the rise (1,000 feet) but you don't know the run, so you must solve for it by using the ol "A"sq'd + "B" sq'd = "C" sq'd. In this case you know "C" is 21,120 feet and sq'd that is 44,605,440. "B" is 1,000 feet and sq'd becomes 1,000,000. Subtract "B"sq'd from "C"sq'd and you get 43,605,440. Now solve for the square root of 43,605,440 and you get 6603 feet. The rise 1,000 feet over the run 6,603 feet gives us a % grade 6.6 (arrived at by dividing the run 6,603 by the rise 1,000).
There I'm pretty sure that's right, if it isn't somebody will correct me.
oooopsBirddog
Jul 16, 2002 6:08 AM
There is some bad math above, my calculater dropped a zero because the number is too long. It should be 446,054,400 and 445,054,400 . I think it actually works out to around a 4.75% grade using those numbers. Sorry, any math people out there?
re: How do you calculate % grades?Breakfast
Jul 15, 2002 9:47 PM
Example:

Let's say you travel 3000 meters, or 3 kilometers and you gain 210 meters in elevation.

210 x 100 = 21,000 vertical distance (VD)
divided by 3000 horizontal distance (HD)

21,000 divided by 3,000 = 7 percent

Metric numbers used for simplicity.
re: How do you calculate % grades?scruffyduncan
Jul 16, 2002 7:00 AM
5% = hill

10% = steep hill

20% = lung burster

25%+ = get off and push