counterclockwise

Counterclockwise, often abbreviated CCW, denotes the direction of rotation or angular change opposite to the motion of clock hands when viewed from the front. The reference orientation can vary by viewpoint, so CCW is defined relative to a chosen perspective, typically a plane or axis.

In the standard two-dimensional Cartesian plane, angular measures increase counterclockwise. Starting from the positive x-axis, a positive angle rotates toward the positive y-axis. For example, moving from (1,0) to (0,1) is a counterclockwise rotation. The opposite direction is clockwise (CW).

Common spellings include counterclockwise and CCW in American usage, while British usage often uses anticlockwise or anti-clockwise. The meaning remains the same across variants, though regional preferences differ.

In physics and engineering, CCW is tied to orientation conventions. The right-hand rule states that a counterclockwise rotation around a given axis corresponds to a positive angular velocity vector along that axis.

Applications of CCW appear in mathematics, computer graphics, and engineering. In the complex plane, multiplication by e^{i theta} rotates a point by theta in the CCW direction. In robotics and animation, specifying CCW versus CW determines how parts rotate around joints or how images are transformed on screen.

See also: clockwise.