Slope Percent and Slope Angle
Slope refers to the angle, or grade, of an incline. Slope can be upward or downward.
Slope is typically expressed as a percent, and corresponds to the amount of rise, or vertical distance, divided by the run, or horizontal distance. Percentage means per 100. Slope can also be expressed as an angle, which gives the amount of deviation from flat as a number of
degrees. Conversions between slope percent and slope angle can be done using a scientific calculator and the inverse tangent (arc tan) function. Essentially, the slope angle is the inverse tangent of the slope percent (with slope percent expressed in decimal).
Example 1 - The slope percent is 60 percent. What is the slope angle?
Measuring Slope Percent
Slope percent can be measured using a clinometer or slope meter, or by dividing the rise by run, as described in this multimedia tutorial. Click the graphic below to view the lesson, which includes audio.
If you have a clinometer or other digital device for measuring slope percent in the field, sight the clinometer as outlined below:
Example 2 - Use the rise and run measurements in the figure below to estimate the slope percent.
Slope percent = (8 feet / 40 feet) × 100 = 0.20 × 100 = 20%
The slope percent is 20 percent.
Calculating Horizontal Distance
If the slope and the vertical distance (rise) are known, then the horizontal distance (run) can be calculated. The slope percent equation can be rearranged to provide the equation for the horizontal distance.
The hill has a horizontal distance of 188 feet.
Calculating Slope Distance
Slope distance (h) is the length of slope from the bottom to the top of the slope and is larger than both the vertical and horizontal distance.
Example 4 - Find the slope distance for the vertical and horizontal distances illustrated in the figure below.
Exercise 1 - Tom has a clinometer on a 5.0-foot pole. He sights another 5.0-foot pole that is 24.0 feet away (horizontal distance). He gets a reading of 20.0 slope percent. What are the slope and vertical distances?
1. What equation should you use to calculate the vertical distance?
The correct answer is a. Rearranging the slope equation slope = rise/run × 100, we find that rise = slope/100 × run
2. What is the vertical distance?
The correct answer is is b. rise = 20/100 × 24. = 4.8 ft.
3. What equation should you use to solve for the slope distance?
The correct answer is b. The slope distance is equal to the square root of the sum of the rise squared + the run squared.
4. What is the slope distance?
The correct answer is c, 24.5 ft. 4.82 + 24.02 = 599.04. The square root of 599.0 is 24.5.