The grade (also called slope, incline, gradient, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number indicates higher or steeper degree of "tilt". Often slope is calculated as a ratio of "rise" to "run", or as a fraction ("rise over run") in which run is the horizontal distance (not the distance along the slope) and rise is the vertical distance. Slopes of existing physical features such as canyons and hillsides, stream and river banks and beds are often described as grades, but typically grades are used for human-made surfaces such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle routes. The grade may refer to the longitudinal slope or the perpendicular cross slope. There are several ways to express slope: as an angle of inclination to the horizontal. (This is the angle α opposite the "rise" side of a triangle with a right angle between vertical rise and horizontal run.) as a percentage, the formula for which is which is equivalent to the tangent of the angle of inclination times 100. In Europe and the U.S. percentage "grade" is the most commonly used figure for describing slopes. as a per mille figure (‰), the formula for which is which could also be expressed as the tangent of the angle of inclination times 1000. This is commonly used in Europe to denote the incline of a railway. It is sometimes written as mm/m instead of the ‰ symbol. as a ratio of one part rise to so many parts run. For example, a slope that has a rise of 5 feet for every 1000 feet of run would have a slope ratio of 1 in 200. (The word "in" is normally used rather than the mathematical ratio notation of "1:200".) This is generally the method used to describe railway grades in Australia and the UK. It is used for roads in Hong Kong, and was used for roads in the UK until the 1970s.

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Railway track
A railway track (British English and UIC terminology) or railroad track (American English), also known as a train track or permanent way, is the structure on a railway or railroad consisting of the , fasteners, railroad ties (sleepers, British English) and ballast (or slab track), plus the underlying subgrade. It enables trains to move by providing a dependable surface for their wheels to roll upon. Early tracks were constructed with wooden or cast iron rails, and wooden or stone sleepers; since the 1870s, rails have almost universally been made from steel.
Cut (earthworks)
In civil engineering, a cut or cutting is where soil or rock from a relative rise along a route is removed. The term is also used in river management to speed a waterway's flow by short-cutting a meander. Cuts are typically used in road, rail, and canal construction to reduce the length and grade of a route. Cut and fill construction uses the spoils from cuts to fill in defiles to cost-effectively create relatively straight routes at steady grades. Cuts are used as alternatives to indirect routes, embankments, or viaducts.
Cut and fill
In earthmoving, cut and fill is the process of constructing a railway, road or canal whereby the amount of material from cuts roughly matches the amount of fill needed to make nearby embankments to minimize the amount of construction labor. Cut sections of roadway or rail are areas where the roadway has a lower elevation than the surrounding terrain. Fill sections are elevated sections of a roadway or trackbed. Cut and fill takes material from cut excavations and uses this to make fill sections.
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