1. What is Slope?

Slope represents the steepness or incline of a surface, typically expressed as a ratio of vertical rise to horizontal run. It can be calculated from an angle in degrees using trigonometric functions.

2. How to Calculate Slope from Degrees

The primary formula for calculating slope from degrees is:

Where:

• \( \theta \) — Angle in degrees
• \( \tan \) — Tangent trigonometric function

Explanation: The tangent of an angle in a right triangle equals the ratio of the opposite side (rise) to the adjacent side (run). This ratio gives us the slope value.

3. Practical Applications

Details: Slope calculations are essential in civil engineering, road construction, roofing, wheelchair ramps, and any application where incline measurement is required.

4. Using the Calculator

Tips: Enter the angle in degrees (0-89.9°). The calculator will automatically compute the slope as a decimal value. For angles approaching 90°, slopes become extremely steep.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between degrees and slope percentage?
A: Slope percentage = tan(θ) × 100%. For example, a 45° angle gives 100% slope.

Q2: What is the maximum slope for common applications?
A: Wheelchair ramps: 4.8° (8.4% slope), Vehicle ramps: 15° (26.8% slope), Stairs: 30-45° (57.7-100% slope).

Q3: How do I convert slope back to degrees?
A: Use the inverse tangent function: θ = arctan(slope) in degrees.

Q4: Why can't I enter 90 degrees?
A: At 90°, the slope is undefined (infinite) as it represents a vertical surface.

Q5: What's the difference between slope ratio and slope percentage?
A: Slope ratio is expressed as rise:run (e.g., 1:4), while slope percentage is (rise/run)×100%.