Degrees to Radians Converter

An angle measures an amount of rotation, and its SI unit is the radian — the angle you get when the arc length equals the radius, so a full circle is exactly 2π radians. Everyday work uses degrees, which split a circle into 360 parts (a legacy of Babylonian base-60 counting); each degree is 60 arcminutes and each arcminute is 60 arcseconds, the fine divisions used in astronomy, navigation and GPS coordinates. Gradians (or gons) offer a metric alternative that divides the circle into 400, handy in surveying because a right angle is a round 100 gon. A full turn or revolution equals 360°, 2π radians or 400 gon, and it can be split into familiar fractions: the quadrant (90°), sextant (60°), octant (45°), the zodiac sign (30°), the compass point (11.25°) and the astronomical hour angle (15°). The military mil is used for range and elevation — NATO divides the circle into 6,400 mils and the former Warsaw Pact into 6,000, both close to a milliradian, which is why a mil subtends roughly one metre at a thousand metres. Binary degrees (256 to a circle) turn up in computing. Radians are the natural choice in mathematics and physics because they make the calculus of sine and cosine come out cleanly. Every unit is stored as its exact number of radians, so any conversion is just the input turned into radians and then into the target unit.