Can anyone share an easy formula for calculating the percentage grade on hills?
If I knew the distance between the bottom and top, (say 5000ft) and vertical climb between bottom and top (say, 200 ft), how do you turn that into a percentage?
is the pythagorean theorem involved in this calculation??
Just divide vertical climb by the horizontal distance and multiply by 100 to get the percentage. For your example, 200/5000*100=4% grade.
Spelling has it right.
To use your example:
(200 / 5 000) * 100 = 4%
Technically, it depends what you mean by "the distance between the bottom and top." If it's the horizontal leg adjacent to the incline angle, then the previous posters have supplied the correct answer. If the distance refers to the hypotenuse (i.e. the 5000' was measured using an odometer), then the Pythagorean Theorem is required. However, for small climbs, the difference between these two cases is negligible. Let "a" be the horizontal distance, "b" be the vertical climb, and "c" be the length of the hypotenuse.
a^2+b^2=c^2
a=sqrt(c^2-b^2)=sqrt(5000^2-200^2)= 4996 ft
%Grade=b/a*100%= 4.003%= 4% (significant figures)
So, in your case, we effectively get the same answer. If you want the value of the incline angle itself, take the arctangent of b/a.
GPS FOO!