1. What is the Slope to Degrees Formula?

The Slope to Degrees Formula converts a slope value (rise over run) into an angle measurement in degrees. This conversion is essential in various fields including engineering, construction, and mathematics where angle measurements are more intuitive than slope ratios.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

Where:

• \( \theta \) — Angle in degrees
• \( \text{slope} \) — Slope value (rise/run)
• \( \arctan \) — 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 using the standard conversion factor.

3. Importance of Angle Calculation

Details: Converting slope to degrees is crucial for practical applications such as roof pitch determination, road gradient analysis, wheelchair ramp design, and various engineering calculations where angular measurements are preferred over ratios.

4. Using the Calculator

Tips: Enter the slope value (rise divided by run). For example, a slope of 1 represents a 45-degree angle, while a slope of 0.5 represents approximately 26.57 degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between slope and angle?
A: Slope is the tangent of the angle. A 45-degree angle has a slope of 1, meaning rise equals run.

Q2: What is the maximum angle this calculator can handle?
A: The calculator can handle any real slope value, producing angles from -90° to +90° (excluding vertical slopes).

Q3: How accurate is the conversion?
A: The conversion is mathematically exact. The calculator provides results rounded to 2 decimal places for practical use.

Q4: Can I use this for negative slopes?
A: Yes, negative slopes will produce negative angles, representing downward inclines.

Q5: What are common slope values and their corresponding angles?
A: Slope 0 = 0°, slope 0.5 ≈ 26.57°, slope 1 = 45°, slope 2 ≈ 63.43°, slope ∞ = 90° (vertical).