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The grade (also called slope, incline, gradient, 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 gradient in calculus where zero indicates ''gravitational level''. 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 and ''rise'' is the vertical distance. The grades or slopes of existing physical features such as canyons and hillsides, stream and river banks and beds are often described. Grades are typically specified for new constructions (such as roads, landscape grading, roof pitches, railroads, aqueducts, and pedestrian or bicycle circulation routes). ==Nomenclature== 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 could also be expressed as the tangent of the angle of inclination times 100. In the U.S., this percentage "grade" is the most commonly used unit for communicating slopes in transportation (streets, roads, highways and rail tracks), surveying, construction, and civil engineering. # 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. # 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 100 feet of run would have a slope ratio of 1 in 20. (The word "in" is normally used rather than the mathematical ratio notation of "1:20"). This is generally the method used to describe railway grades in Australia and the UK. Any of these may be used. Grade is usually expressed as a percentage, but this is easily converted to the angle α from horizontal or the other expressions. Slope may still be expressed when the horizontal run is not known: the rise can be divided by the hypotenuse (the slope length). This is not the usual way to specify slope; it follows the sine function rather than the tangent function, so it calls a 45-degree slope a 71-percent grade instead of a 100-percent. But in practice the usual way to calculate slope is to measure the distance along the slope and the vertical rise, and calculate the horizontal run from that. When the angle of inclination is small, using the slope length rather than the horizontal displacement (i.e. using the sine of the angle rather than the tangent) makes only an insignificant difference. Railway gradients are usually expressed in terms of the rise in relation to the distance along the track as a practical measure. In cases where the difference between sin and tan is significant, the tangent is used. In Europe, road gradients are signed as a percentage, the exception being Britain, where for road signs, maps and construction work, the gradient was traditionally expressed as a ratio such as 1 in 12, but signs showing gradient as a percentage are becoming more common.〔(Highway code: Warning signs )〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grade (slope)」の詳細全文を読む スポンサード リンク
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