form , where k is the measure of a complete turn expressed in the chosen unit (for example, for degrees or 400 grad for gradians): The value of thus defined is independent of the size of the circle: if the length of the radius is changed then the arc length changes in the same proportion, so the ratio s/r is unaltered. Angle addition postulate The angle addition postulate states that if B is in the interior of angle AOC, then The measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC. Units Throughout history, angles have been measured in various units. These are known as angular units, with the most contemporary units being the degree ( ° ), the radian (rad), and the gradian (grad), though many others have been used throughout history. Most units of angular measurement are defined such that one turn (i.e. the angle subtended by the circumference of a circle at its centre) is equal to n units, for some whole number n. Two exceptions are the radian (and its decimal submultiples) and the diameter part. In the International System of Quantities, angle is defined as a dimensionless quantity, and in particular the radian unit is dimensionless. This convention impacts how angles are treated in dimensional analysis. For a discussion see . The following table list some units used to represent angles. Signed angles Although the definition of the measurement of an angle does not support the concept of a negative angle, it is frequently useful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions relative to some reference. In a two-dimensional Cartesian coordinate system, an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis, while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns. With positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward the negative y-axis. When Cartesian coordinates are represented by standard position, defined by the x-axis rightward and the y-axis upward, positive rotations are anticlockwise and negative rotations are clockwise. In many contexts, an angle of −θ is effectively equivalent to an angle of "one full turn minus θ". For example, an orientation