A gradient is usually used to measure how steep or how gentle the slope is. In other words, it measures the rate at which the slope is rising/falling. However, due to the fact that the surface of the land is rarely uniform, gradient measures the average steepness of the slope of a piece of land.
With the help of contours, the gradient of a given slope or a terrain feature can be conveniently determined from a topographic map. This article will show you how to determine gradient from a topographic map, how to express it and, how to interpret it.
DETERMINING GRADIENT OF A SLOPE ON TOPOGRAPHIC MAPS
In order to calculate the gradient of a slope, the Vertical Increase (rise), as well as the Horizontal Equivalent (run) of the two points, need to be first determined.
Procedures for Determining Gradient on Topographic Maps (A Step-By-Step Guide)

Step 3: Determine the horizontal equivalent.
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The horizontal equivalent is 4km |
Step 4: Determine the elevations of each of these points, and then calculate the Vertical Increase.
Therefore;
() = 3050 − 1850 = 1200.
Step 6: Calculate the gradient of a slope.
Gradient can be expressed either as a percentage, an angle, or a proportion.
a) Gradient Expressed In Proportions
In terms of proportion, a gradient is found by simply dividing the Vertical Increase and the Horizontal Equivalent.
For the example above;
b) Gradient Expressed In Percentage
The gradient of a slope expressed in percentage is obtained by multiplying the quotient of the Vertical Increase and the Horizontal Equivalent by 100%.
Therefore, the gradient of the slope is 30%.
The gradient of a slope expressed in degrees is calculated by using the arctangent of the quotient of the Vertical Increase and the Horizontal Equivalent.
For the example above;
Therefore, the gradient of the slope is 16.7°.
INTERPRETING GRADIENT OF A SLOPE
The interpretation of the gradient of a slope usually varies from one industry to another. While a gradient of 12% is considered moderate enough for bike racing, it is extremely steep for the adhesive railways. Also, a gradient of 30% can be considered extremely steep for agricultural activities, but it is not steep enough for the funicular railways.
For describing the relief of an area or a terrain, the gradient is usually interpreted as shown in the table below;
Gradient (in %) | Interpretation |
0% – 2% | Little or no slope |
3% – 15% | Gentle slope |
16% – 35% | Moderate slope |
36% – 100% | Steep slope |
Greater than 100% | Extremely steep slope |
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Interpreting the gradient of a slope when describing the relief |
APPLICATION OF GRADIENT OF SLOPES IN REAL LIFE
Engineers, architects, developers, military soldiers, geologists, environmentalists, farmers and other field experts often use the knowledge of gradient of slopes to perform and assess various tasks in their fields of work. The following are some areas of interest in which the knowledge of gradient of slopes is often applied;