Convert Slope To Angle Calculator

Conversion Formula:

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

Angle:

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1. What is Slope to Angle Conversion?

The slope to angle conversion calculates the angle (in degrees) that corresponds to a given slope (rise over run). This is commonly used in engineering, construction, and mathematics to understand the steepness of a surface.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

\( \text{Slope} \) — The ratio of vertical rise to horizontal run (unitless)
\( \arctan \) — The inverse tangent function
\( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The arctangent function converts the slope ratio to an angle in radians, which is then converted to degrees.

3. Importance of Slope-Angle Conversion

Details: Understanding the angle equivalent of a slope is crucial for construction safety, road design, wheelchair ramp accessibility, and various engineering applications.

4. Using the Calculator

Tips: Enter the slope value (rise/run) in the input field. The slope can be any real number (positive or negative). The calculator will return the 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 degree measurement of inclination.

Q2: What does a 100% slope equal in degrees?
A: A 100% slope (1:1 ratio) equals 45 degrees.

Q3: Can I convert angle back to slope?
A: Yes, slope = tan(angle), where angle is in degrees.

Q4: What's the maximum possible angle?
A: Theoretically 90° (vertical), but practically most applications consider up to about 60°.

Q5: How accurate is this conversion?
A: Mathematically exact, though real-world measurements may have practical limitations.