What percentage of grade corresponds to a 45-degree angle?

The correct answer, which indicates that a 45-degree angle corresponds to a grade of 100 percent, is based on the relationship between angle and grade in civil engineering and construction.

When translating an angle of elevation or slope into a percentage grade, the formula used is:

Grade (%) = tan(angle in degrees) * 100.

For a 45-degree angle, the tangent (tan) is equal to 1. Thus:

Grade (%) = tan(45 degrees) * 100 = 1 * 100 = 100 percent.

This means that for every 100 units of horizontal distance, the elevation changes by 100 units, resulting in a 1:1 slope. Understanding this concept is crucial in excavation, grading, and surfacing work, as it guides decisions on equipment, safety, and material management on job sites.