Grade (geography)
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In topography, the pitch of a slope (such as a hill, roof, path, road) is often referred to as its grade (or gradient, especially in the UK). A grade is measured by a number where zero indicates level (with respect to gravity) and increasing numbers correlate to more vertical inclinations.
| angle | tangent | sine |
|---|---|---|
| 0° | 0% | 0% |
| 5° | 9% | 9% |
| 10° | 18% | 17% |
| 30° | 58% | 50% |
| 45° | 100% | 71% |
| 60° | 173% | 87% |
| 90° | ∞ | 100% |
There are three common numbering systems: the angle from horizontal in degrees, or as a percentage. There are two systems using the percentage.
The usual mathematical definition is the tangent of the angle of inclination: the ratio of the altitude change to the horizontal distance. However, an alternative definition is the sine of the angle: the ratio of the altitude change to the surface length between any two points on the grade—also known as rise to run.
The difference between the two is small for gentle slopes (see small-angle formula). The ambiguities and the small differences that result may permit these two inconsistent approaches to coexist unrecognized, especially where grades considered are 15% or less.
Many of the mathematical principles of slope, that follow from the definition, are applicable in topographic practice. Grade is usually expressed as a percentage. Expressing it as the angle from horizontal carries the same information, but may lead to confusion for readers who are not proficient in trigonometry: they may confuse degree with percent, and/or not know how to do the conversion. In the UK, for road signs, maps and construction work, the gradient is often expressed as a ratio such as 1 in 12, or as a percentage [1].
In vehicular engineering, various land-based designs (cars, SUVs, trucks, trains, etc.) are rated for their ability to ascend terrain. (Trains typically rate much lower than cars.) The highest grade a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability").
