arctanhellingsgraad100

Arctanhellingsgraad100 is a term used to describe the angle obtained when converting a slope grade of 100 percent into an angle with the arctangent function. In Dutch engineering usage, hellingsgraad refers to slope expressed as a percentage, where a grade of 100 percent means a rise of 1 unit for every 1 unit of run.

The core relation is θ = arctan(grade/100), where θ is the angle in either radians or degrees depending on the mode of the arctangent function. For a 100 percent grade, θ = arctan(100/100) = arctan(1) = 45 degrees. This illustrates how a 100 percent slope corresponds to a 45-degree incline. For reference, a 50 percent grade yields θ ≈ arctan(0.5) ≈ 26.57 degrees, and a 200 percent grade yields θ ≈ arctan(2) ≈ 63.43 degrees.

In practice, arctanhellingsgraad100 and its related concept are used to translate design tolerances and safety criteria between percentages and geometric tilt in road, railway, and ramp design. The inverse relationship is grade% = tan(θ) × 100, allowing engineers to convert an angle back into a slope percentage.

Notes on implementation: many calculators and programming environments return the arctangent in radians by default; to express the result in degrees, multiply the output by 180/π or set the calculator to degree mode. The concept highlights the link between linear grade measurements and angular slope.