Еңіс өлшемі

Angle to the horizontal plane
the grade of a topographic feature or constructed element

The grade (US) or gradient (UK) (also called stepth, slope, incline, 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 the word "grade" is 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.

Grades are related using the following equations with symbols from the figure at top.

For degrees, percentage (%) and per mille (‰) notations, larger numbers are steeper slopes. For ratios, larger numbers n of 1 in n are shallower, easier slopes. The examples show round numbers in one or more of the notations and some documented and reasonably well known instances. + Examples of slopes in the various notations Degrees Percentage (%) Permillage (‰) Ratio Remarks 60° 173% 1732‰ 1 in 0.58 47.7° 110% 1100‰ 1 in 0.91 Stoosbahn (funicular railway) 45° 100% 1000‰ 1 in 1 30.1° 58% 580‰ 1 in 1.724 Lynton and Lynmouth Cliff Railway (funicular railway) 30° 58% 577‰ 1 in 1.73 25.5° 47% 476‰ 1 in 2.1 Pilatus Railway (steepest rack railway) 20.3° 37% 370‰ 1 in 2.70 Mount Washington Cog Railway (maximum grade) 20° 36% 363‰ 1 in 2.75 18.4° 33% 333‰ 1 in 3 16.9° 30% 300‰ 1 in 3.3 Extremely steep road 14.0° 25% 250‰ 1 in 4 Very steep road. Mount Washington Cog Railway (average grade) 11.3° 20% 200‰ 1 in 5 Steep road 8.13° 14.2% 142‰ 1 in 7 7.12° 12.5% 125‰ 1 in 8 Cable incline on the Cromford and High Peak Railway 5.71° 10% 100‰ 1 in 10 Steep road 4.0° 7% 70‰ 1 in 14.3 3.37° 5.9% 59‰ 1 in 17 Swannington incline on the Leicester and Swannington Railway 2.86° 5% 50‰ 1 in 20 Matheran Hill Railway. The incline from the Crawlerway at the Kennedy Space Center to the launch pads. 2.29° 4% 40‰ 1 in 25 Cologne–Frankfurt high speed rail line 2.0° 3.5% 35‰ 1 in 28.57 LGV Sud Est, LGV Est, LGV Méditerranée 1.97° 3.4% 34‰ 1 in 29 Bagworth incline on the Leicester and Swannington Railway 1.89° 3.3% 33‰ 1 in 30.3 Rampe de Capvern on the display=1 1.52° 2.65% 26.5‰ 1 in 37.7 Lickey Incline 1.43° 2.5% 25‰ 1 in 40 LGV Atlantique, LGV Nord. The Schiefe Ebene. 1.146° 2% 20‰ 1 in 50 Railway near Jílové u Prahy. Devonshire Tunnel 0.819° 1.43% 14.3‰ 1 in 70 Waverley Route 0.716° 1.25% 12.5‰ 1 in 80 Ruling grade of a secondary main line. Wellington Bank, Somerset 0.637° 1.11% 11.11‰ 1 in 90 Dove Holes Tunnel 0.573° 1% 10‰ 1 in 100 The long drag on the Settle & Carlisle line 0.458° 0.8% 8‰ 1 in 125 Rampe de Guillerval 0.2865° 0.5% 5‰ 1 in 200 display=1, except for the rampe de Guillerval 0.1719° 0.3% 3‰ 1 in 333 0.1146° 0.2% 2‰ 1 in 500 0.0868° 0.1515% 1.515‰ 1 in 660 Brunel's Billiard Table Didcot to Swindon 0.0434° 0.07575% 0.7575‰ 1 in 1320 Brunel's Billiard Table Paddington to Didcot 0° 0% 0‰ 1 in ∞ (infinity) Flat

In vehicular engineering, various land based designs (automobiles, sport utility vehicles, trucks, trains, etc.) are rated for their ability to ascend terrain. Trains typically rate much lower than automobiles. The highest grade a vehicle can ascend while maintaining a particular speed is sometimes termed that vehicle's "gradeability" (or, less often, "grade ability"). The lateral slopes of a highway geometry are sometimes called fills or cuts where these techniques have been used to create them. In the United States, maximum grade for Federally funded highways is specified in a design table based on terrain and design speeds, with up to 6% generally allowed in mountainous areas and hilly urban areas with exceptions for up to 7% grades on mountainous roads with speed limits below
The steepest roads in the world according to the Guinness Book of World Records are Baldwin Street in Dunedin, New Zealand, Ffordd Pen Llech in Harlech, Wales and Canton Avenue in Pittsburgh, Pennsylvania. The Guinness World Record once again lists Baldwin Street as the steepest street in the world, with a 34.8% grade (1 in 2.87) after a successful appeal against the ruling that handed the title, briefly, to Ffordd Pen Llech. A number of streets elsewhere have steeper grades than those listed in the Guinness Book. Drawing on the U. S. National Elevation Dataset, 7x7 (magazine) identified ten blocks of public streets in San Francisco open to vehicular traffic in the city with grades over 30 percent. The steepest at 41 percent is the block of Bradford Street above Tompkins Avenue in the Bernal Heights neighborhood. The San Francisco Municipal Railway operates bus service among the city's hills. The steepest grade for bus operations is 23.1% by the 67 Bernal Heights on Alabama Street between Ripley and Esmeralda Streets. The street has formed part of a bicycle race since 1983.

Grade, pitch, and slope are important components in landscape design, garden design, landscape architecture, and architecture; for engineering and aesthetic design factors. Drainage, slope stability, circulation of people and vehicles, complying with building codes, and design integration are all aspects of slope considerations in environmental design.

Gradients on sharp curves are effectively a bit steeper than the same gradient on straight track, so to compensate for this and make the ruling grade uniform throughout, the gradient on those sharp curves should be reduced slightly.

In the era before they were provided with continuous brakes, whether air brakes or vacuum brakes, steep gradients made it extremely difficult for trains to stop safely. In those days, for example, an inspector insisted that Rudgwick railway station in West Sussex be regraded. He would not allow it to open until the gradient through the platform was eased from 1 in 80 to 1 in 130.