slope angle

The slope angle α of any line in 2 is the angle between ( the line and x-axis; in the case that the line is descending, the angle is negative. We always have that -90<α90.

For all non-vertical lines having a slope of m, the slope angle is


and we also have that


Below are some examples of slope angles of lines that intersect the x-axis.

...α|α|xxpositive αnegative α

In some mathematical works, the slope angle of a line in 2 is defined to be the angle measured from the positive x-axis to the line in the counterclockwise direction. This definition has some drawbacks because slope angles are then allowed to be obtuse but can no longer be negative. When this definition is used, the α=arctanm no longer holds. The convention in PlanetMath is to use the former definition.


  • 1 “Slope, Distance and Equation Calculator.” 1729 Software Systems. Accessed on 24 June 2007. URL:
  • 2 “Slope angle.” McGraw-Hill Dictionary of Scientific and Technical Terms. McGraw-Hill Companies, Inc., 2003. Accessed via on 7 June 2007. URL:
Title slope angle
Canonical name SlopeAngle
Date of creation 2013-03-22 17:13:14
Last modified on 2013-03-22 17:13:14
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 22
Author Wkbj79 (1863)
Entry type Definition
Classification msc 53A04
Classification msc 51N20
Related topic Slope
Related topic LineInThePlane
Related topic ZeroesOfDerivativeOfComplexPolynomial