1. What is Slope Angle?

The slope angle is the angle between a slope surface and the horizontal plane, calculated as the arctangent of the slope ratio (rise over run). It's commonly expressed in degrees, minutes, and seconds (DMS) format for precision.

2. How Does the Calculator Work?

The calculator uses the arctangent function:

Where:

• \( \theta \) — Angle in degrees
• \( S \) — Slope (rise/run, unitless)

Explanation: The calculator first computes the angle in decimal degrees, then converts it to DMS format (degrees° minutes' seconds").

3. Importance of Slope Angle Calculation

Details: Slope angle calculations are essential in civil engineering, construction, road design, geology, and various outdoor activities like hiking and skiing.

4. Using the Calculator

Tips: Enter the slope value (rise divided by run) as a unitless number. For example, a 10% grade would be entered as 0.10.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between slope percentage and slope angle?
A: Slope percentage is rise/run × 100, while slope angle is the arctangent of rise/run expressed in degrees.

Q2: How precise is the DMS conversion?
A: The calculator shows seconds rounded to the nearest whole number, providing precision to about 1/60th of a minute.

Q3: What's the maximum slope angle possible?
A: Theoretically 90° (vertical), though most practical slopes are much less. A 45° angle equals a 100% slope (1:1 ratio).

Q4: Why use DMS format instead of decimal degrees?
A: DMS provides more precise measurements for applications like surveying and engineering where small angle differences matter.

Q5: How does this relate to gradient?
A: Gradient is typically expressed as a ratio (like 1:20) or percentage, while angle is the actual inclination measurement.