# How to Find the Percentage of a Grade

Calculation of the grade of a slope in a percentage form is needed in many engineering and drainage applications. For example, warning signs are used in hilly areas where downward grades exceed 4 percent for an extended distance. The warning signs tell motorists and truck drivers to slow down or use a low gear to control speed. The grade of slope is also needed when perfroming grading work or when laying pipe for drainage. Minimum slope grades of 0.5% to 1.0% are needed to promote positive drainage. Finding the percentage of grade is actually an easy calculation.

## Calculating Percent Grade from Coordinates

Using coordinates is often preferred by surveyors and those who lay out construction grading for a project. Coordinates are typically provided in a state plane system using northing and easting values with an elevation value. To show an example of calculating percent grade from coordinates, simple x,y, and z values are used here:

Point 1: 200, 50, 87

Point 2: 295, 75, 90

- First the horizontal distance between the two points is determined using the x and y values of the coordinates.

The following formula is used, based on the point coordinates given.

SQRT((295-200)^{2}+(75-50)^{2)}= 98.23

- Next, determine the elevation difference from the coordinates. It is the difference in the z values so 90-87= 3
- The grade is calculated by dividing the elevation difference by the horizontal distance.

grade = 3/98.23 = .0305

- To get the grade in percent form multiply the grade by 100.

.0305 x 100 = 3.05 percent grade

## Determining Percent Grade Slope wth a Level

A level is a valuable tool in determining percent grade of a slope. Here is the way it works.

- Place either a standard level or a sting line level on a slope.
- Get the level exactly horizontal (level)
- Measure the distance from each end of the bottom of the level to the ground
- Measure the length of the level
- The percent grade is the difference in distance from the bottom of each end of the level divided by the length of the level multiplied by 100..

A string line level is used to measure a percent slope grade over a longer distance. Smart Levels are also available which have a digital display which shows the percent slope grade when the smart level is placed on the ground. This provides a direct reading with no calculation of grade required.

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