Quarterturns

Quarterturns, or quarter-turns, refer to a rotation of an object by 90 degrees about a fixed axis. It is one fourth of a full rotation, and in radians it equals pi/2. In two-dimensional settings, successive quarter-turns about the same center produce a sequence of orientations that cycle every four turns.

In mathematics and computer graphics, quarter-turns are used to describe and compose orientations, rotations, and symmetry operations. They are a basic unit of angular change and can be combined to achieve arbitrary directions. On a clock or compass, a quarter-turn corresponds to moving a reference direction by 90 degrees—for example, rotating from north to east.

In mechanical and industrial contexts, quarter-turns are common in devices designed for quick, simple operation. Quarter-turn valves, such as ball and butterfly valves, use a 90-degree rotation to switch between open and closed states. Similarly, quarter-turn latches and fasteners employ a 90-degree rotation to secure or release components. These mechanisms are favored for their reliability, ease of use, and clear open/closed positions.

In puzzle culture, the quarter-turn metric (QTM) counts each 90-degree face turn on a Rubik’s Cube as a single move, while 180-degree turns count as two moves. This metric contrasts with the half-turn metric, which treats 180-degree turns as a single move.

Related concepts include half-turns (180 degrees) and full turns (360 degrees).