>
> > Then there are 'grades,' used on roads and probably elsewhere. For example, occasionally one sees signs warning of "6% grade next 10 miles" or something similar. What is grade?
> >

After looking through various sources, it seems there are two ways to define the grade of a road: you can define it as in my last post (rise over run), which would be the tangent of the inclination angle, or the rise over the road length, which would be the sine of the inclination angle.

Under the first definition, a 6% grade would correspond to an angle of about 3.434 degrees, and under the second definition, it would correspond to an angle of about 3.440 degrees. For small grades, the definitions will nearly coincide. I suspect that since they're rounding to the nearest percentage of grade when they tell you it's 6%, they're losing all hope of precision, so it doesn't matter which definition they used to measure the grade.