The average gradient calculator determines the steepness of a slope, often known as the grade. This is defined by the relationship between the vertical change (Rise) and the horizontal distance (Run) between two points.

1. Calculating Slope Gradient

To calculate the slope gradient, you divide the change in vertical height by the change in horizontal distance. The fundamental formula is:

Where:

• $\text{Rise}$ = Vertical difference between the highest and lowest points.
• $\text{Run}$ = Horizontal distance between the points.

2. Calculating Slope Angle

The angle of a slope is commonly expressed in degrees. To find this, you must use the arctangent function on the gradient ratio.

This calculation converts the dimensionless slope ratio into an angle ($\theta$) in degrees.

3. How to Calculate the Slope of a Hill

For practical field applications, such as surveying a hill, follow these steps:

• Measure Distance: Measure the horizontal distance (or map distance) between the top and bottom of the hill.
• Find Altitude Difference: Using a map or GPS, determine the elevation at both the top and bottom points.
• Unit Conversion: Ensure both the distance and altitude measurements are in the same units (e.g., both in meters or both in feet).
• Calculate: Divide the difference in altitude by the horizontal distance.

Note: This assumes a linear increase. If the slope varies significantly, calculate the gradient for sections where the slope is relatively constant.

4. The Linear Function ($y = mx + b$)

In mathematics, the "function of a slope" describes the linear relationship between variables, typically denoted as $y = mx + b$.

Where:

• $y$ = Dependent variable (output)
• $x$ = Independent variable (input)
• $m$ = The slope (Rate of change of $y$ with respect to $x$)
• $b$ = Y-intercept (Value of $y$ when $x$ is 0)

5. Summary of Slope Representations

Slopes can be represented in various formats depending on the industry (Construction, Road Works, Mathematics).