Editing Slope (section)

== Slope of a road or railway ==
{{main|Grade (slope)|Grade separation}}
There are two common ways to describe the steepness of a [[road]] or [[rail tracks|railroad]]. One is by the angle between 0° and 90° (in degrees), and the other is by the slope in a percentage. See also [[steep grade railway]] and [[rack railway]].

The formulae for converting a slope given as a percentage into an angle in degrees and vice versa are: 
: <math>\text{angle} = \arctan \left( \frac{\text{slope}}{100\%} \right)</math> (this is the inverse function of tangent; see [[trigonometry]])
and
: <math>\mbox{slope} = 100\% \times \tan( \mbox{angle}),</math>
where ''angle'' is in degrees and the trigonometric functions operate in degrees. For example, a slope of 100[[percent sign|%]] or 1000[[per mil|‰]] is an angle of 45°.

A third way is to give one unit of rise in say 10, 20, 50 or 100 horizontal units, e.g. 1:10. 1:20, 1:50 or 1:100 (or "1 ''in'' 10", "1 ''in'' 20", etc.) 1:10 is steeper than 1:20. For example, steepness of 20% means 1:5 or an incline with angle 11.3°.

Roads and railways have both longitudinal slopes and cross slopes.

<gallery>
File:Nederlands verkeersbord J6.svg|Slope warning sign in the [[Netherlands]]
File:PL road sign A-23.svg|Slope warning sign in [[Poland]]
File: Skloník-klesání.jpg|A 1371-meter distance of a railroad with a 20[[Per mil|‰]] slope. [[Czech Republic]]
File: Railway gradient post.jpg|Steam-age railway gradient post indicating a slope in both directions at [[Meols railway station]], United Kingdom
</gallery>