Rise Run to Degrees Calculator

How to Calculate Angle from Rise and Run

Converting rise and run (or slope) to an angle in degrees is a common task in various fields, including construction, engineering, and physics. This calculation helps determine the steepness of an incline or the angle of elevation.

Rise Run to Degrees Formula

The formula to convert rise and run to degrees is:

\[ \theta = \arctan\left(\frac{\text{Rise}}{\text{Run}}\right) \times \frac{180°}{\pi} \]

Where:

• θ (theta) is the angle in degrees
• Rise is the vertical change
• Run is the horizontal change
• arctan is the inverse tangent function
• We multiply by (180°/π) to convert radians to degrees

Calculation Steps

1. Determine the rise (vertical change) and run (horizontal change)
2. Calculate the ratio of rise to run
3. Apply the arctan function to this ratio
4. Convert the result from radians to degrees by multiplying by (180°/π)

Example Calculation

Let's calculate the angle for a slope with a rise of 3 units and a run of 4 units.

1. Rise = 3, Run = 4
2. Calculate the ratio: \[ \frac{\text{Rise}}{\text{Run}} = \frac{3}{4} = 0.75 \]
3. Apply the arctan function: \[ \arctan(0.75) \approx 0.6435 \text{ radians} \]
4. Convert to degrees: \[ 0.6435 \times \frac{180°}{\pi} \approx 36.87° \]

Therefore, the angle of the slope is approximately 36.87°.

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the rise, run, and angle for the example above:

This diagram illustrates the rise (vertical change), run (horizontal change), and the resulting angle formed with the horizontal plane.