1. What is Slope Angle Calculation?

Slope angle calculation converts the ratio of vertical rise to horizontal run into an angle measured in degrees. This is commonly used in engineering, construction, and geography to describe the steepness of slopes.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \( \theta \) — Slope angle in degrees
• \( Slope \) — Ratio of rise over run
• \( \arctan \) — Inverse tangent function
• \( \pi \) — Mathematical constant (approximately 3.1416)

Explanation: The arctangent function converts the slope ratio to an angle in radians, which is then converted to degrees using the 180/π conversion factor.

3. Importance of Slope Angle

Details: Slope angle calculations are essential for road design, roof construction, wheelchair ramps, ski slopes, and geological assessments. Proper slope angles ensure safety, functionality, and compliance with building codes.

4. Using the Calculator

Tips: Enter the slope as a ratio (rise divided by run). For example, a 1:4 slope would be entered as 0.25. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slope ratio and slope angle?
A: Slope ratio expresses steepness as a proportion (rise:run), while slope angle expresses it in degrees from horizontal.

Q2: What are common slope angle ranges?
A: Gentle slopes: 0-15°, moderate slopes: 15-30°, steep slopes: 30-45°, very steep: 45°+.

Q3: How accurate is this calculation?
A: The calculation is mathematically precise for the given inputs, using standard trigonometric functions.

Q4: Can I use this for percent grade calculations?
A: Percent grade = slope × 100%. To convert percent grade to degrees, use the same formula with percent/100 as the slope.

Q5: What are practical applications of slope angle?
A: Road design (maximum 6-8° for highways), roof construction, wheelchair accessibility (max 4.76°), and geological hazard assessment.