Calculate Angular Product
Calculator for multiplication and division of angles in different notations. An angle can be entered as decimal degrees, in degrees, arc minutes and arc seconds (° ′ ″), as radian or as multiples of Pi (π). As results, the angles in all of these notations will be displayed. The total result is the calculated angles, the corrected result is the angles in the range between 0 and 360 degrees, respectively 2π. The rotations in the corrected result indicate how many times a complete rotation was performed, i.e., how many times 360 degrees were omitted from this result.
Decimal degrees, degrees, arcminutes and arcseconds, radians, and multiples of π are different ways to express an angle. The calculated values for these in each of the three sections always mean the same thing. π corresponds to 180 degrees, as radians, this is 3.14159... 60 arcseconds equal one arcminute, 60 arcminutes equal one degree, or π/180. Expressing angles in radians or as multiples of π is often used in scientific contexts, while expressing them in degrees is more generally understood.
Which angular product, the total or the corrected one, is more relevant depends on the application. If only the direction in which the angle points is of interest, then the corrected result without rotations is the one sought. The complete result, on the other hand, contains information about the direction of the angle, the number of rotations, and the direction in which the rotation occurred. This information is contained in a single value, which can then be arbitrarily large. The corrected result with the rotations also contains all the information about the resulting rotation, but distributed across two values. What is lost in both results is the information about the number of individual rotations and angles, these are the factors of the multiplication.