When you travel through the mountains, it is very common to see signs that say things like, "Trucks check brakes -- 10% grade" or "6% grade -- Trucks use right lane only".
The percent grade is a simple calculation. Let's say you have a road up a hill, and the road is 1,000 feet long. In that 1,000 feet it rises 100 feet. 100 divided by 1,000 is 0.10, or 10%. It doesn't really matter if it is feet, meters, miles or kilometers -- if you know how far the road rises or falls in a given distance, you can calculate the percent grade by dividing the rise or fall by the distance.
If you are familiar with the trigonometry functions, you recognize that what you are calculating when you divide the rise by the distance is the tangent of an angle. Therefore, to calculate the number of degrees when you know the percent grade, you simply take the arctangent of the grade. So, if it is a 10% grade, you take the arctan of 0.10 and you find that the angle is 5.7 degrees.
Roads are probably measured in percent grade rather than degrees for two reasons:
- You don't have to have a special calculator or trig tables to calculate percent grade
- If you know the percent grade, it is very easy to calculate the distance you have risen or fallen simply by looking at your odometer. If you have coasted down a mile long hill on a 10% grade, you know you have fallen a tenth of a mile in vertical height.