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"Grade" describes the steepness of a hill. The steepness of the hill results in the change in elevation over a given horizontal distance. A gently sloping hill changes elevation very gradually from the base of the hill to the top of the hill while a steep hill changes elevation over a much shorter distance. The steepness of the hill can be described as the percent slope or as angle of the slope. A topographic map is a useful tool for calculating hill grade as it depicts elevation through the use of contour lines in addition to horizontal distance.

Items you will need

• Pencil

• Paper

• Topographic map

• Calculator with trigonometric function

Identify the hill on the topographic map to be measured. Draw a line from the base of the hill to the top of the hill (or at least the portion of the hillside to be traveled).

Determine the elevation at the base of the hill. Contour lines on the topographic map connect adjacent points of similar elevation. Contour lines appear as dark brown index contour lines, light brown intermediate contour lines, and dashed brown supplementary contour lines.

Find the elevation at the top of the hill. Contour lines will provide the elevation information needed to make this determination. Additionally, some hills and mountain tops will have a specific elevation value marked at their top.

Subtract the elevation of the base of the hill from the elevation at the top of the hill to find the change in elevation.

Measure the horizontal distance between the base of the hill and the top of the hill.

Divide the change in elevation by the horizontal distance then multiply by 100 to produce the percent slope (vertical distance/horizontal distance x 100 = % slope).

Calculate the angle of the slope by dividing the change in elevation by the horizontal distance to yield the tangent of the slope angle. The inverse tangent (arctangent) of this value will produce the angle of the slope.

Tips

• It is important to select the appropriate side and section of the hill of interest. Many hills vary in grade on different sides.