1. What is Slope Percentage?

Slope percentage represents the ratio of vertical rise to horizontal run, expressed as a percentage. It's commonly used in engineering, construction, and road design to describe incline steepness.

2. How Does the Conversion Work?

The conversion uses the trigonometric tangent function:

Where:

• \( \theta \) — Angle in degrees
• \( \tan \) — Trigonometric tangent function

Explanation: The tangent of an angle in a right triangle equals the ratio of the opposite side (rise) to the adjacent side (run). Multiplying by 100 converts this ratio to a percentage.

3. Practical Applications

Details: Slope percentage is used in road design (maximum grades), wheelchair ramp construction (typically 8.33% max), roof pitches, and trail grading.

4. Using the Calculator

Tips: Enter angle in degrees (0-90). The calculator will compute the equivalent percentage slope. 45° equals 100% slope (rise equals run).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between degrees and percentage slope?
A: Degrees measure angle directly, while percentage expresses the ratio of vertical to horizontal distance.

Q2: What percentage is a 30 degree slope?
A: Approximately 57.74% (tan(30°) × 100).

Q3: Is there a maximum possible percentage slope?
A: As angle approaches 90°, percentage slope approaches infinity (tan(90°) is undefined).

Q4: How steep is a 10% slope?
A: About 5.71° (arctan(0.10)).

Q5: Why use percentage instead of degrees?
A: Percentage is often more intuitive for practical applications like construction and engineering.