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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, in order to calculate the grade (100% × rise/run) or standard slope (rise/run).
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.
When distances are measured along the slope, the equivalent horizontal distance may be determined by applying a slope correction. The vertical slope angle of the length measured must be measured. (Refer to the figure on the other side) Thus, For gentle slopes, < % =
The world average river reach slope is 2.6 m/km or 0.26%; [2] a slope smaller than 1% and greater than 4% is considered gentle and steep, respectively. [3] Stream gradient may change along the stream course. An average gradient can be defined, known as the relief ratio, which gives the average drop in elevation per unit length of river. [4]
For a 1 degree shift at 1 NM, there are about 100 feet of offset. This becomes very useful for estimating or correcting vertical speed settings and flight path angles (FPA) during climb, descent, or approaches. If a gradient in % is required, the numbers work out with the same rule: 1% over 1 NM ≈ 60'
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Typically on straight road sections, the drainage gradient is at least 1–3% due to the normal cross slope of 1–3%. In curved sections the drainage gradient is higher, and may often reach 5–12% due to superelevated CS that may reach 5–8% in areas with icy roads and up to 12% in areas without icy roads.