1. What is Slope in Degrees?

Slope in degrees represents the angle of inclination of a line relative to the horizontal axis. It's calculated from the ratio of vertical change (rise) to horizontal change (run) between two points.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( y₂, y₁ \) — y-coordinates of two points (in meters)
• \( x₂, x₁ \) — x-coordinates of two points (in meters)
• \( \arctan \) — Inverse tangent function
• \( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The formula first calculates the tangent of the angle as rise over run, then converts this to an angle in degrees.

3. Importance of Slope Calculation

Details: Slope calculations are essential in engineering, construction, road design, and geography. They help determine the steepness of terrain, proper drainage angles, and structural stability.

4. Using the Calculator

Tips: Enter coordinates of two points in meters. The calculator will determine the angle of the line connecting them. Vertical lines (undefined slope) will be indicated.

5. Frequently Asked Questions (FAQ)

Q1: What does a 45° slope mean?
A: A 45° slope means the line rises 1 unit vertically for every 1 unit horizontally (100% grade).

Q2: What's the difference between slope in degrees and percentage?
A: Degrees measure the angle, while percentage is rise/run × 100. 45° = 100% grade.

Q3: What's considered a steep slope?
A: In construction, slopes >30° are considered steep. For roads, >10% (≈5.7°) is steep.

Q4: How to interpret negative slope values?
A: Negative values indicate downward slopes (declines) when moving left to right.

Q5: What's the maximum possible slope angle?
A: The theoretical maximum is 90° (vertical line), though the calculator shows this as "undefined".