1. What is the Slope to Degrees Formula?

The Slope to Degrees Formula converts slope percentage to angle in degrees using trigonometric principles. This conversion is essential in various fields including engineering, construction, and geography where angle measurements are more intuitive than slope percentages.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( \theta \) — Angle in degrees
• \( Slope \) — Slope percentage
• \( \arctan \) — Inverse tangent function
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The formula first converts slope percentage to a decimal ratio (slope/100), then calculates the arctangent to get the angle in radians, and finally converts radians to degrees.

3. Importance of Slope Conversion

Details: Converting slope percentage to degrees is crucial for accurate angle measurements in construction, road design, roofing, and various engineering applications where precise angular measurements are required.

4. Using the Calculator

Tips: Enter the slope percentage value. The calculator will automatically compute the corresponding angle in degrees. Valid input values are non-negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slope percentage and degrees?
A: Slope percentage represents vertical rise per 100 units of horizontal run, while degrees represent the actual angle from horizontal.

Q2: What is a 100% slope in degrees?
A: A 100% slope equals a 45-degree angle, as tan(45°) = 1 = 100/100.

Q3: Can slope percentage exceed 100%?
A: Yes, slopes can exceed 100% (angles greater than 45 degrees), representing steeper inclines.

Q4: Where is this conversion commonly used?
A: Commonly used in civil engineering, architecture, road construction, wheelchair ramp design, and ski slope grading.

Q5: How accurate is this conversion?
A: The mathematical conversion is exact. Accuracy depends on the precision of the input slope value and the calculator's rounding.