To convert a gradient to a slope:
\[ S = \arctan\left(\frac{G}{100}\right) \times \left(\frac{180}{\pi}\right) \]
Where:
Gradient is a measure of how steep a slope is, expressed as a percentage. It represents the vertical change divided by the horizontal change between two points on a line. In other words, it is the rise over the run, multiplied by 100 to get a percentage.
Slope is the angle between the horizontal plane and the line of interest. It is often measured in degrees and is used in various fields such as engineering, surveying, and construction to describe the steepness of a hill or incline.
Let's assume the following value:
Step 1: Divide the gradient by 100:
\[ \frac{G}{100} = \frac{25}{100} = 0.25 \]
Step 2: Take the arctangent of the result:
\[ \arctan(0.25) \approx 0.24498 \text{ radians} \]
Step 3: Convert radians to degrees by multiplying by \(\frac{180}{\pi}\):
\[ S = 0.24498 \times \frac{180}{3.14159} \approx 14.04 \text{ degrees} \]
