Slope Angle Calculator Degrees Formula

Slope Angle Formula:

\[ \text{Angle (deg)} = \arctan(\text{Slope}) \times \left(\frac{180}{\pi}\right) \]

Angle (deg):

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1. What is the Slope Angle Formula?

The Slope Angle Formula converts a slope ratio (rise over run) into an angle in degrees. This is useful in various fields like engineering, construction, and geography.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Angle (deg)} = \arctan(\text{Slope}) \times \left(\frac{180}{\pi}\right) \]

Where:

Slope — The ratio of vertical rise to horizontal run (unitless)
arctan — The inverse tangent function
180/π — Conversion factor from radians to degrees

Explanation: The formula calculates the angle whose tangent is the given slope value, then converts it from radians to degrees.

3. Importance of Slope Angle Calculation

Details: Calculating slope angles is essential for designing ramps, roads, roofs, and other inclined surfaces to ensure safety and proper functionality.

4. Using the Calculator

Tips: Enter the slope value (rise/run ratio). The calculator will compute the corresponding angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between slope and angle?
A: Slope is a ratio (rise/run) while angle is the actual inclination measured in degrees.

Q2: What's the maximum possible slope angle?
A: Theoretically 90° (vertical), though practical applications rarely exceed 45°.

Q3: How does this relate to percentage grade?
A: Percentage grade = slope × 100. A 100% grade equals a 45° angle.

Q4: Can I calculate slope from angle?
A: Yes, slope = tan(angle in degrees × π/180).

Q5: When is this calculation most useful?
A: For construction projects, wheelchair ramp design, road engineering, and topographic analysis.