Rise and Run to Degrees Calculator

What is Rise and Run?

Rise and run are terms used to describe the vertical and horizontal components of a slope. The rise is the vertical change, while the run is the horizontal change. Together, they define the steepness of a slope.

In construction, this information is crucial for determining drainage needs, foundation requirements, and material quantities. Engineers and surveyors frequently convert these measurements into degrees to better understand the angle of the slope.

How to Calculate Degrees from Rise and Run

To convert rise and run to degrees, you use the arctangent function. This is a trigonometric function that calculates the angle whose tangent is the ratio of rise to run.

The process involves:

1. Measuring the vertical rise (change in elevation)
2. Measuring the horizontal run (change in distance)
3. Calculating the ratio of rise to run
4. Using the arctangent function to find the angle in radians
5. Converting the radians to degrees

Our calculator handles all these steps automatically, giving you the angle in degrees with just a few clicks.

The Formula Explained

Where:

• rise = vertical change
• run = horizontal change
• arctan = inverse tangent function
• π ≈ 3.14159265359

The formula converts the ratio of rise to run into an angle in degrees. The arctangent function is used because it directly relates the ratio of the opposite side to the adjacent side in a right triangle to the angle.

Worked Example

This means the slope has an angle of approximately 36.87 degrees from the horizontal. This information is useful for determining the appropriate materials and construction techniques for the slope.