Calculate A Slope in Degrees Calculator

Determine the angle of a slope in degrees using our free online calculator. This tool helps you calculate the steepness of a surface based on vertical rise and horizontal run measurements.

How to Use This Calculator

Using our slope in degrees calculator is simple:

Enter the vertical rise (change in height) in the first field.
Enter the horizontal run (change in distance) in the second field.
Click the "Calculate" button to get the slope angle in degrees.
Review the result and use the chart to visualize the slope.

The calculator will display the angle in degrees and show a graphical representation of the slope.

Formula Explained

The angle of a slope is calculated using the arctangent function of the ratio of vertical rise to horizontal run:

slope angle (degrees) = arctan(rise / run) × (180/π)

Where:

rise = vertical change in height
run = horizontal change in distance
π (pi) ≈ 3.14159265359

The result is converted from radians to degrees by multiplying by 180/π.

Worked Examples

Example 1: Roof Slope

If a roof rises 4 feet vertically over a 12 feet horizontal distance:

slope angle = arctan(4/12) × (180/π) ≈ 18.4349 degrees

The roof has an angle of approximately 18.43 degrees.

Example 2: Hiking Trail

For a trail that ascends 30 meters vertically over a 100 meters horizontal distance:

slope angle = arctan(30/100) × (180/π) ≈ 16.7046 degrees

The trail has a slope angle of approximately 16.70 degrees.

Frequently Asked Questions

What is a slope in degrees?: A slope in degrees measures the steepness of a surface relative to the horizontal. It's calculated using the arctangent of the ratio of vertical rise to horizontal run.
How do I measure the rise and run?: Use a measuring tape to measure the vertical change (rise) and horizontal distance (run) between two points on the slope.
What does a 45-degree slope mean?: A 45-degree slope is a diagonal line where the vertical rise equals the horizontal run, creating a 1:1 ratio. It's as steep as it is wide.
Can I use this calculator for construction projects?: Yes, this calculator is useful for construction professionals to determine slope angles for ramps, roofs, and other structural elements.
What if my slope is very steep?: For slopes steeper than 45 degrees, the angle will be greater than 45 degrees. The calculator will still provide an accurate measurement.