degrees to [percent

[drudnick]

Hi, I have slope measurements in degrees, and I want to know how to convert them to percent (gradient) and vice versa. Ah, age and the loss of trigonometric skills! I appreciate the assistance.

Sincerely,

DR

[Knight]

Hi, I have slope measurements in degrees, and I want to know how to convert them to percent (gradient) and vice versa. Ah, age and the loss of trigonometric skills! I appreciate the assistance.

First, lets look at how we determine what the the slope of a line in geometry, or of a slanted surface such as a road or a roof in practical geometry, is the ratio of the "rise" to the "run." This might be presented as a fraction or a decimal:

Code: Select all

         +              +                      +
        / |             /|                   /  |
      /   |6           / |6               /     |3
    /     |           /  |             /        |
  +-------+          +---+          +-----------+
      6                3                  9

  slope=6/6=1     slope=6/3=2       slope=3/9=1/3

A slope can also be presented as a percentage, which is really just a special fraction whose denominator is 100, as indicated by the "%" symbol. The three slopes above are then 100%, 200%, and 33 1/3 % respectively (obtained by multiplying each slope by 100%).

We can also talk about the ANGLE of a slope, which is the angle of the slanted line above the horizontal. This is related to the slope itself by trigonometry: the slope is the tangent of the angle.

Code: Select all

          +              +                      +
        / |             /|                   /  |
      /   |6           / |6               /     |3
    /45   |           /63|             /18      |
  +-------+          +---+          +-----------+
      6                3                  9

  angle=45 deg    angle=63.4 deg      angle=18.4 deg

So, the trigonometry magic that you are looking for is the tangent. If you know the angle, take the tangent it, and you will get the slope of the angle. If you multiply the slope by 100, you'll have the percentage of slope.