A 6 percent grade of a road translates to an angle of approximately 3.43 degrees.
To understand how we convert percentage grades to degrees, we need to know what a grade represents. A grade of 6 percent means that for every 100 units of horizontal distance, the elevation changes by 6 units. This is usually expressed as a ratio of the rise over the run.
To find the angle in degrees, we can use the tangent function, which is defined in a right triangle as the ratio of the opposite side (rise) to the adjacent side (run). In this case, the tangent of the angle will be equal to the grade expressed as a decimal.
The formula we use is:
angle (degrees) = arctan(grade)
For a 6 percent grade, we first convert the percentage to a decimal by dividing by 100:
6 percent = 0.06
Now, we apply the arctan function:
angle = arctan(0.06)
Using a calculator, we find:
angle ≈ 3.43 degrees
This means that a road with a 6 percent grade rises relatively gently, making it manageable for vehicles to navigate.