Grade (slope)
Grade measures steepness as angle, percentage, or ratio.
Grade (or gradient), also called slope, incline, mainfall, pitch, or rise, is a measure of the steepness of a physical feature, landform, or constructed line. It is expressed as the elevation angle to the horizontal or its tangent, with zero indicating horizontality and larger numbers indicating steeper tilt. Commonly calculated as a ratio of rise (vertical distance) to run (horizontal distance), grade is used for human-made surfaces such as roads, railroads, and roofs, while natural features like canyons and hillsides are also described by grades.
- field
- Engineering, Geography, Transportation
- known_for
- Measuring steepness of roads, railways, and landforms
- common_expressions
- Percentage, per-mille, ratio (1 in n), angle in degrees
- steepest_recorded_street
- Baldwin Street, Dunedin, New Zealand (34.8% grade, 1 in 2.87)
- maximum_us_federal_highway_grade
- Up to 6% generally, with exceptions for 7% on mountainous roads below 60 mph
Lore & Background
Grade is expressed in several ways: as an angle of inclination to the horizontal; as a percentage (100 × rise/run); as a per-mille figure (1000 × rise/run); or as a ratio of one part rise to so many parts run (e.g., 1 in 200). In Europe and the U.S., percentage grade is most common for describing slopes, while per-mille is used for railway inclines in Europe. The ratio method is typical for railway grades in Australia and the UK, and was used for UK roads until the 1970s. When the horizontal run is unknown, slope may be calculated using the slope length and vertical rise, approximating the sine function, though the tangent is standard for accuracy.
Reader's Guide
Grade is a critical concept in vehicular engineering, where vehicles are rated for their ability to ascend terrain, known as 'gradeability.' In the United States, federally funded highways have maximum grades specified by design tables, with up to 6% allowed in mountainous areas and hilly urban zones, and exceptions for 7% on roads with speed limits below 60 mph. The steepest streets in the world, according to Guinness World Records, include Baldwin Street in Dunedin, New Zealand (34.8% grade), Ffordd Pen Llech in Harlech, Wales, and Canton Avenue in Pittsburgh, Pennsylvania. However, other streets, such as Bradford Street in San Francisco, have grades over 41%. The San Francisco Municipal Railway operates bus service on grades up to 23.1%. Grade is also used for landscape grading, roof pitches, aqueducts, and pedestrian routes, and is expressed in signage as a percentage in Europe.
Did You Know?
- Grade can be expressed as an angle, percentage, per-mille, or ratio (e.g., 1 in 200).
- A 45-degree slope equals a 100% grade.
- The steepest street in the world per Guinness World Records is Baldwin Street in Dunedin, New Zealand, with a 34.8% grade.
- In the U.S., federally funded highways generally allow up to 6% grade in mountainous areas, with exceptions for 7% on roads below 60 mph.
Frequently Asked Questions
What is Grade (slope) in physical geography?
Grade is a numerical way to express how steep a surface tilts relative to the horizontal plane. It can be stated as an angle in degrees, a percentage, a per-mille value, or a simple '1 in n' ratio. Both natural landforms like canyon walls and built structures like roads are commonly described using this measure.
How do you calculate Grade (slope)?
You divide the vertical rise by the horizontal run to get the ratio, then convert that into whichever expression you need—percentage, degrees, or a 1-in-n figure. A value of zero means the surface is perfectly flat, while higher numbers indicate a more dramatic tilt.
What is the steepest recorded street grade in the world?
Baldwin Street in Dunedin, New Zealand, holds the record at roughly 34.8 percent, which translates to about a 1-in-2.87 ratio. That makes it the most extreme example of a public road built on a natural slope.
What grade limits apply to U.S. federal highways?
The general maximum is 6 percent for standard routes, though mountainous sections with posted speed limits below 60 mph may be permitted up to 7 percent. These caps exist to keep vehicles controllable on long climbs and descents.
Which fields rely on Grade (slope) measurements?
Engineering, geography, and transportation all depend on grade to design safe roads, railways, and rooftops. Natural-feature studies—like mapping hillside erosion or canyon profiles—also use the same steepness calculations.
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