A ruled surface, in geometry, is one generated by a straight line, called a generatrix, when moving over one or more curved or straight lines, called guidelines. Depending on the particular characteristics and conditions of these elements, it receives various names.

Ruled surfaces are:

A surface "Surface (mathematical)") is ruled if for each point on it, there is a straight line containing a and contained in . A ruled surface can always be represented (at least locally) by a parametric equation of the following form:.

where is a curve on , and is a curve on the unit sphere. So, for example,

a surface containing the Möbius Strip is obtained.

Alternatively, a ruled surface can be represented parametrically as:.

Where and are two curves that do not intersect. For example, when y move with constant velocity along two warped lines, the surface is a hyperbolic paraboloid, or part of a single-sheet hyperboloid.