Convert between different angle units including degrees, radians, and gradians.
Angles measure the rotation between two lines that share a common endpoint (vertex). Different systems have been developed throughout history to measure angles, each with specific applications in mathematics, navigation, surveying, and engineering.
The most familiar unit for measuring angles. A full circle contains 360 degrees. This system originated in ancient Babylon, where a base-60 number system was used. The choice of 360 is convenient because it has many divisors (1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360), making it easy to divide circles into equal parts.
The standard unit in mathematics and physics. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle contains 2π radians (approximately 6.283). Radians are dimensionless and essential for calculus, as derivatives of trigonometric functions are simplest when angles are in radians.
Also called gons or grades, this system divides a right angle into 100 gradians, making a full circle 400 gradians. Used primarily in surveying and some European countries, gradians make it easy to work with percentages of a right angle.
Subdivisions of degrees used for precise measurements. One degree equals 60 arc minutes, and one arc minute equals 60 arc seconds. These units are essential in astronomy, navigation, and geodesy for measuring celestial positions and coordinates.