Slope percent is important in figuring how to contour land. A 1/2-percent slope is used for applications that involve drainage of land and concrete, such as patios and sidewalks. It also figures significantly in conservation farming irrigation, where the land most vulnerable to rain erosion gets a 1/2-percent slope. The formula for calculating a 1/2-percent slope can be approached in at least two ways. You can solve for the rise or the run.
Solve for Rise
Learn the formula for slope percent: slope percent = (rise/run) x 100
Learn the components of the formula. The run is the level distance measured from the higher side of the land used to the lower side. The rise is the distance up from the level of the lower side to the higher side at the highest point. The percent slope is the ratio of the rise and run, converted to a percentage by multiplying by 100.
Fill in the formula with the numbers you have. In this case the slope percent will be one half or 0.5. Insert the run number in the formula as well. If the run is 120 feet, the formula becomes 0.5 = (rise/120) x 100.
Rearrange the formula to solve for the rise. Divide each side by 100. This changes the equation to: 0.005 = (rise/120). Multiply each side by 120. This gives you this equation: 0.005 x 120 = rise.
Solve the equation 0.005 x 120 = rise, or rise = 0.6 feet. Convert the rise into inches. 0.6 feet = 0.6 x 12 inches = 7.2 inches. The rise is 7.2 inches.
Solve for Run
Start with the basic formula: percent slope = (rise/run) x 100. Fill in the values you have. With the one-half percent slope in mind, given a 9-inch rise, the formula to find the run would be: 0.5 = (9 inches/run) x 100. However, run is measured in feet, so it must be converted.
Convert rise inches to feet. With 12 inches in a foot, nine inches would be 9/12 of a foot, or 3/4 of a foot, or 0.75 feet. If the numbers are not so obvious, divide the rise inches by 12 to get the feet, so 9/12 = 0.75. Recast the formula using feet, so 0.5 = (.75/run) x 100.
Divide each side by 100, yielding 0.005 = 0.75/run. Multiply each side by run to get the following equation: 0.005 x run = .75. Divide each side by 0.005. The resulting equation is run = 0.75/.005, so run = rise/(slope percent/100).
Solve for the run using the resulting equation, which is run = 0.75/0.005. Where rise = 9 inches and slope = 0.5 percent, the run will be 150 feet.