1. What is Slope to Angle Conversion?

Slope to angle conversion is a mathematical process that converts the slope of a line (rise over run) into an angle measured in degrees. This is commonly used in geometry, trigonometry, engineering, and construction to determine the inclination of surfaces.

2. How Does the Calculator Work?

The calculator uses the inverse tangent function:

Where:

• \( \text{slope} \) — Ratio of vertical rise to horizontal run
• \( \arctan \) — Inverse tangent function
• \( \frac{180}{\pi} \) — Conversion factor from radians to degrees

Explanation: The arctangent function calculates the angle whose tangent equals the given slope, then converts the result from radians to degrees for practical use.

3. Importance of Angle Calculation

Details: Accurate angle calculation is essential for construction projects, road design, roof pitch determination, wheelchair ramp design, and various engineering applications where precise inclinations are required.

4. Using the Calculator

Tips: Enter the slope value as a unitless ratio (rise/run). For example, a slope of 0.5 means 1 unit rise for every 2 units run. Positive values indicate upward slope, negative values indicate downward slope.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between slope and angle?
A: Slope is a ratio (rise/run) while angle is measured in degrees. Slope describes steepness numerically, while angle describes it geometrically.

Q2: What does a slope of 1 mean in degrees?
A: A slope of 1 (45° angle) means the rise equals the run, creating a perfect diagonal.

Q3: Can I calculate angle from percentage grade?
A: Yes, percentage grade divided by 100 gives the slope. For example, 25% grade = 0.25 slope.

Q4: What is the maximum angle possible?
A: Theoretically, angles range from -90° to 90°, but practical applications typically use angles between 0° and 45°.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise. Accuracy depends on the precision of your slope measurement.