for math people - an easy way to calculate grade of a hill?

No trig needed http://wiki.answers.com/Q/How_do_you_grade_a_hill_level

If it climbs 1 foot for every 100 feet of horizontal distance, it is a 1% grade. Thus a climb of 52.8' per mile is a 1% grade, 105.6 feet per mile is 2%, etc. A 100% grade would be 100 feet of climbing for 100 feet of horizontal distance or a slope of 45 degrees.

hillbilly wrote:

Vertical height of hill, taken from contours on a topo map

The guys above have mentioned the equation you use to calculate the grade, but failed to mention how you determine the horizontal distance term in the equation. You can get the horizontal distance a few ways:

Horizontal Distance = SquareRoot(Hypotenuse^2-Vertical^2)

Also, if you have a topographical map, can't you just scale off the horizontal distance?

Unless the hill is really steep (and if it's on a road, it probably won't be), the road distance will be good enough for the horizontal distance.

I doubt there are many roads above 20% grade, and even at this grade you'll get something like a 2% error in your estimation of the gradient. That is, if it's actually 20% grade you might instead estimate it to be 19.6% or something. Nothing to worry about.

Yeah, with even what we would consider a steep road grade, the hill is actually so shallow in terms of angle degree that the base and the hypoteneuse are damn close to the same. A hill that climbs 200' per mile would feel very steep, but the actual distance run would only be 5283.7' run on the slope rather than the 5280' base.

Thanks everyone for the info. I think I can do it with this for the big hills around here.

The insight that the hypoteneuse and the horizontal are pretty close is helpful. I am guessing that this approximation works well only if it is a pretty long hill? There's a very short but very steep little hill at our local jr. high that I'm guessing is about a 150 foot run up a vertical rise that looks to be about 30 feet. It looks and feels very steep.

Until I did the math, I too though that the slope would add actual mildly relevant "running" distance until Malmo, among others, set me straight. You do the math and you see it would have to be quite steep to matter.

Road distance is OK wrote:

I doubt there are many roads above 20% grade, and even at this grade you'll get something like a 2% error in your estimation of the gradient. That is, if it's actually 20% grade you might instead estimate it to be 19.6% or something. Nothing to worry about.

There are very few streets with a 20% grade.

One thing to remember is that the human brain tends to overestimate the grade of a hill--so all the steep hills you've seen were not as steep as you thought. Keep that in mind. (In the absolute, that is. Doesn't mean we can't tell which of two angles is sharper.)