Understanding the concept of rise over run is essential for those interested in math, architecture, engineering, and other scientific fields. It’s also a useful skill for any individuals who find themselves needing to determine the slope or steepness of a hill, ramp, roof, or landscape. In this article, we will provide a comprehensive guide on how to calculate rise over run.

What is Rise Over Run?

Rise over run is a concept that applies to linear relationships such as slopes and gradients. It refers to the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. The result of this calculation is used to determine the “slope” or “gradient,” which is a measure of how steep the hill, ramp, roof or landscape is.

Step-by-Step Guide on How to Calculate Rise Over Run

1. Identify Two Points on the Line

To calculate rise over run, we first need two points on the line. These points are often represented in coordinate form as (x1, y1) and (x2, y2).

2. Determine the Rise

The rise refers to the vertical distance between the two points mentioned earlier. To find this value, subtract the y-coordinates of both points:

Rise = y2 – y1

3. Determine the Run

The run refers to the horizontal distance between those same two points. To find this value, subtract the x-coordinates of both points:

Run = x2 – x1

4. Calculate Rise Over Run

Finally, divide the rise by the run to get your slope or gradient:

Slope or Gradient = Rise ÷ Run

Example

Let’s say we have two points on a line: A(3, 6) and B(8, 16). Here’s how you would calculate rise over run:

1. Identify Two Points:

Point A: (3, 6)

Point B: (8, 16)

2. Determine the Rise:

Rise = y2 – y1

Rise = 16 – 6

Rise = 10

3. Determine the Run:

Run = x2 – x1

Run = 8 – 3

Run = 5

4. Calculate Rise Over Run:

Slope or Gradient = Rise ÷ Run

Slope or Gradient = 10 ÷ 5

Slope or Gradient = 2

Conclusion

Learning how to calculate rise over run is relatively simple and has a myriad of practical applications. By following this step-by-step guide and practicing with real-life examples, you will become an expert in calculating slope and understanding linear relationships in no time.