How do you figure out the % grade of a hill? What exactly does it mean?

There are several systems for expressing grade/slope:

as an angle of inclination from the horizontal of a right triangle. (This is the angle α opposite the "rise" side of the triangle.)

as a percentage (also known as the grade), the formula for which is which could also be expressed as the tangent of the angle of inclination times 100. In the U.S., the grade is the most commonly used unit for communicating slopes in transportation, surveying, construction, and civil engineering.

as a per mille figure, the formula for which is which could also be expressed as the tangent of the angle of inclination times 1000. This is commonly used in Europe to denote the incline of a railway.

as a ratio of one part rise per so many parts run. For example, a slope that has a rise of 5 feet for every 100 feet of run would have a slope ratio of 1 in 20.

Any one of these expressions may be used interchangeably to express the characteristics of a slope. Grade is usually expressed as a percentage, but this may easily be converted to the angle α from horizontal since that carries the same information.

There is a method in which slope may be expressed when the horizontal run is not known: rise divided by the hypotenuse (the slope length). This is not a usual way to measure slope. This follows the sine function rather than the tangent function and this method diverges from the "rise over run" method as angles start getting larger (see small-angle formula).

Many of the mathematical principles of slope that follow from the definition are applicable in topographic practice. In the UK, for road signs, maps and construction work, the gradient is often expressed as a ratio such as 1 in 12, or as a percentage.[1]

In civil engineering applications and physical geography, the slope is a special case of the gradient of calculus calculated along a particular direction of interest which is normally the route of a highway or railway road bed.

8% grade means you change 8 feet in elevation over a 100-foot stretch. 8/100=.08=8%

If it is 120 feet in elevation over 400 yards, 120 feet=40 yards. 40/400=.1=10%

not ten degress, 10%. Different symbol different meaning.

the percent is rise / run * 100.

Although you have it completely backwards 10% is steep and 10 degree angle is even steeper about 19%.

inverse tangent (% grade / 100) = degrees

Yes 10 degree is a steep hill on a trail and very steep for a road. Most people have no idea about this and make ridiculous overestimated exaggerations about the angle in degrees of slopes, such as a runners saying he did a hill session on a 30 degree slope, which is just impossible.

indeed wrote:

Yes 10 degree is a steep hill on a trail and very steep for a road. Most people have no idea about this and make ridiculous overestimated exaggerations about the angle in degrees of slopes, such as a runners saying he did a hill session on a 30 degree slope, which is just impossible.

Divide the vertical by the horizontal times 100 to get percentage. I. E. 5 ft vertical rise for 100 ft. is a 5% grade.

Often used in cycling for mountains & hills. Keep in mind that grade is generally an average over the entire run. There are probably portions which are steeper and some more shallow.

-Mt. Washington (road race) 11.6% for 7.6miles / max of 18%

-Koppenberg, Belgium 11.6% on cobbles for 1.25mi / max of 22%

-Alp d' Huez, France (probably most prominent alpine TDF pass) 7.9% for 8.89mi / max of 14%

10 degrees would be a grade of 17.6% (tan 10 deg = 0.176) and yes that is very steep, probably steeper than any road you've run on.

Ronald Templeton wrote:

question........ wrote:

I hear people say "I ran up a 10% grade hill the other day" or "I ran up a 15% grade hill the other day" or for hill repeats, "find a 8% grade hill." etc.

What exactly does it mean? How is the steepness measured? I was originally thinking the angle between the ground and hill, but 10% grade was apparently kind of steep? And 10 degrees angle isn't that steep...

well you see, there is this new system called the common core...

-ronnie

Ronnie, why are you topping threads from 7 years ago? Not to mention, how are you even finding these before deciding to add some seemingly unrelated random ramblings. Are you a new experimental nonsensical TrackBot or something?

For the guy who I'm sure is still wondering about grades from 7 years, and checking daily for a reply, why don't you try setting the treadmill to 10% and see how different it makes a mile feel?

From my experience, I can say even for trail runners who are used to hills, anything above 7% or so is going to feel like a significant hill that really throws your heart rate up. This is assuming a legitimate hill that's at least 200 meters or so, and not just a little blip you run on for 20 seconds. Once you get to about 12% it's something that you're not running for more than 200 meters unless you're specifically doing a hill workout built around that hill. Finally, in my experience, around 20% is when no one is running it unless they're very specifically doing hill repeats where they're form is thrown off and they're stopping at the top to recover.

green lantern wrote:

Often used in cycling for mountains & hills. Keep in mind that grade is generally an average over the entire run. There are probably portions which are steeper and some more shallow.

-Mt. Washington (road race) 11.6% for 7.6miles / max of 18%

-Koppenberg, Belgium 11.6% on cobbles for 1.25mi / max of 22%

-Alp d' Huez, France (probably most prominent alpine TDF pass) 7.9% for 8.89mi / max of 14%

Mount Washington:

GRADE: Average 12%, multiple lengths of 18% sustained, last 50 yards of course are 22%.

Source:

Here are some that I've found difficult, here on the Big Island:

1. 10K trail race, with 1200' over the first 5k, which is about 7%

2. The road I train on regularly, with a 5k section that rises 670', about 4%

3. A 32 mile walk I make sometimes, 8600' climb, about 5%

4. Then there's is the last section of #3, which is 2700' over 6.3 miles, about 8%, and the climb starts at 6700'

5. And finally, the worst part of #4, the 1.55 miles starting at about 8300' and going to 9300', which is at 12%. It's nasty.

Definitely no bragging here. I do this stuff very slowly. If you want long, long climbs -- come and visit me. I'll show you where they are and you can attack them.

Well u say that.... I encountered hills that go up 5 feet for 10 feet of length and I even ran up it, granted it was on a trail and my running I mean getting up over it.

Also I feel there are some people who may not know the spam control

Think Interstate Highways and bridges are built with 6% maximum grade.

So many interesting answers over the years. Does not look like anyone has answered the question directly.

The percentage grade of a hill is the slope written as a percent. If you know how to calculate the slope of a hill then you are almost there. To calculate the slope of a run you divide the rise of the hill by the distance of the run.

Here is an example: The run over 4000ft will rise a total of 80ft so the slope is 80/4000 = 0.02. Written as a percent is 2% .

question........ wrote:

I hear people say "I ran up a 10% grade hill the other day" or "I ran up a 15% grade hill the other day" or for hill repeats, "find a 8% grade hill." etc.

What exactly does it mean? How is the steepness measured? I was originally thinking the angle between the ground and hill, but 10% grade was apparently kind of steep? And 10 degrees angle isn't that steep...

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