What is the ground slope angle formula used to compute slope from vertical and horizontal distances?

• A. VD times 57.3 divided by HD
• B. HD times 57.3 divided by VD
• C. VD divided by HD
• D. VD times 57.3 / HD (ROUND UP ALWAYS)

Answer: (D)

When you want the ground slope angle from how far up and how far across you’ve gone, you’re working with a rise-over-run relationship. The exact way to get the angle in degrees is to take the arctangent of the vertical distance divided by the horizontal distance, then convert from radians to degrees. That would be θ(deg) = arctan(VD/HD) × 57.2958.

In field practice, a quick estimate is often used: for small slopes, tan θ ≈ θ (in radians). So θ ≈ VD/HD (in radians), and converting to degrees gives θ ≈ (VD/HD) × 57.3. This is a practical approximation, which is why the option that uses VD × 57.3 ÷ HD aligns with that method. The “ROUND UP ALWAYS” instruction is added to keep the assessment conservative—always err on the side of safety by not underestimating the slope.

So this option is best because it reflects the common field approach: convert the VD/HD ratio to degrees using the 57.3 factor and then round up to avoid underestimating slope hazards. The other choices either invert the ratio, give a radian value without conversion, or omit the rounding rule, which reduces safety or accuracy in practice.