circle Unit Converter
Definition of circle unit
As an angular unit, a circle represents one complete revolution about a point. It equals 360 degrees, 2π radians, 400 gradians, or one turn; fractions of a circle express proportional rotations, such as a semicircle equaling 180 degrees.
History of circle unit
The circle is among humanity’s oldest mathematical forms, appearing in early astronomy, surveying, calendars, and engineering. Ancient Babylonian mathematicians used a sexagesimal system that helped establish divisions of a full turn into 360 degrees. Greek scholars, especially Hipparchus and Ptolemy, developed geometric and astronomical angle calculations. The radian emerged much later from eighteenth- and nineteenth-century mathematical analysis, becoming the natural angle unit because it relates an angle directly to the arc length it subtends. Modern angle converters therefore commonly connect circles, degrees, radians, gradians, and turns.
Applications of circle unit
In an angle converter, “circle” denotes one complete revolution, useful for expressing rotations in robotics, navigation, mechanics, animation, and graphic design. For example, 0.25 circle equals a quarter-turn, 0.5 circle equals a half-turn, and 1 circle equals 360 degrees or 2π radians. It also helps compare turn-based measurements intuitively across different systems.
Complete list of circle unit conversion
- degree [°] = 0.0027777777777778 circle
- radian [rad] = 0.1591549430919 circle
- grad [^g] = 0.0025 circle
- minute ['] = 4.6296296296296E-5 circle
- second ["] = 7.716049382716E-7 circle
- gon = 0.0025 circle
- sign = 0.083333333333333 circle
- mil = 0.00015625 circle
- revolution [r] = 1 circle
- turn = 1 circle
- quadrant = 0.25 circle
- right angle = 0.25 circle
- sextant = 0.16666666666667 circle
