Calculating the slope of land is useful for geological, topographical and architectural applications. Slope is important for surveying land and mapping, determining whether or not a construction team can work in a certain area and how long it will take to construct lines underground. The slope of land is more complicated than the y = mx + b equation from basic algebra. It can be expressed either as an angle or a percentage, but the calculations remain the same. You'll need a topographic map to make your calculations.
Choose the area on the map where you want to calculate the slope. You must choose an area where the direction of the slope remains the same, not the top of a hill or the bottom of a valley.
Draw a straight line that is perpendicular to the contours on this area of your map in the area you want to measure. Start and end your line on, rather than between, the contours on the map.
Measure the line you drew. Use the scale on the map to convert its distance into feet.
Calculate the total elevation change along the line. Note the elevation of the lowest and highest contours on the line, and subtract the elevation of the lowest contour from the elevation of the highest contour.
Divide the total change in elevation in feet by the distance of the line in feet. This gives you the tangent value for the slope. To determine the angle of the slope, enter the tangent value into a scientific calculator, and hit the "inv" and "tan" buttons.
To determine the per cent slope of the land, multiply the tangent value by 100.
Things you need
- Topographic map
- Scientific or graphing calculator