Directional Angle Display and Calculation
Shows the direction of a given angle. Angles can be entered and calculated in degrees, rad and π. Please adjust the angle with a controller or enter a value and press Show direction and convert. The other values will be calculated and the change of direction is marked with the arrow. Values between -360° and 360° can be processed, which is a full turn left or right.
90 degrees or π/4 corresponds to a quarter turn to the right. -270 degrees is a three-quarter turn to the left, pointing in the same direction as 90 degrees. With 180 degrees, it doesn't matter for the direction whether the rotation is left or right. 180 degrees and -180 degrees point in the same direction. 360 degrees is a full turn and therefore points in the same direction as 0 degrees.
Directional angles are used when not only the magnitude of an angle, but above all its orientation and direction of rotation are relevant. This is when rotations with a sign or directed movements need to be described unambiguously and comprehensibly. Unlike opening angles, they clearly describe the direction of a rotation and its extent.
Such angle specifications are common in navigation, for example, for courses, bearings, or directions of movement. Here, north is usually defined as 0 degrees. Directional angles are also used in physics and engineering to define rotational movements, the orientation of components, or the directions of forces and velocities.
In mathematics, particularly in vector calculus and trigonometry, directional angles serve to describe the position of vectors, lines, or planes relative to a fixed reference direction. Positive and negative angles allow for a clear distinction between left and right rotations.
In computer science, for example, in computer graphics, simulation, or robotics, directional angles allow rotations to be represented, combined, and interpreted consistently, even when multiple full rotations occur. For directions in space, see also quaternions.