Converter category
Angle Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, turns, milliradians, and compass points.
Universal Angle Converter
About angle conversions
Angle conversions are used in mathematics, navigation, astronomy, engineering, surveying, and computer graphics. Our angle converter covers degrees, radians, gradians, arcminutes, arcseconds, turns, milliradians, and compass points. Whether you are solving trigonometry problems, setting a miter saw, reading a compass, programming rotation, or studying celestial coordinates, this converter provides precise angle conversions based on the exact relationships between units.
Most popular angle conversions
Available units
Popular angle conversions (8 total)
Unit definitions
Degree (°)
A degree is 1/360 of a circle. Used worldwide for angles and temperature.
Origin: Babylonians used base-60 number system, dividing circle into 360 degrees.
Current use: Navigation, Geometry, Weather (temperatures)
Radian (rad)
A radian is the angle where the arc length equals the radius. SI unit of angle.
Origin: Roger Keyes introduced radian in 1873. SI accepted in 1960.
Current use: Mathematics, Physics, Engineering
Gradian (grad)
A gradian is 1/400 of a circle (100 grads = 90°). Used in surveying.
Origin: Introduced in France in 1795 as part of metric system.
Current use: Surveying, Masonry, Military artillery
Arcminute (')
An arcminute is 1/60 of a degree (1° = 60'). Used in navigation and astronomy.
Origin: Part of Babylonian base-60 number system.
Current use: Astronomy, Navigation, Optics
Arcsecond (")
An arcsecond is 1/3600 of a degree (1° = 3600"). Used in astronomy.
Origin: Further division of base-60 Babylonian system.
Current use: Astronomy, GPS, Ballistics
Turn (tr)
A turn (revolution) equals 360° or 2π radians. Full circle rotation.
Origin: Revolution standardized as a measurement unit.
Current use: Mechanical engineering, Motors, Rotating machinery
Milliradian (mrad)
A milliradian is 1/1000 of a radian. Used in ballistics and artillery.
Origin: MILspec used by military for artillery calculations.
Current use: Ballistics, Artillery, Optics adjustment
Compass Point (pt)
A compass point is 1/32 of a circle, equal to 11.25°. Traditional navigation.
Origin: Wind rose divided into 32 points in medieval navigation.
Current use: Marine navigation, Aviation, Wind direction
Common uses for angle conversions
Angle conversions are used in trigonometry, navigation, astronomy, carpentry, machining, computer graphics, surveying, and physics.
Frequently asked questions about angle
How many radians are in 180 degrees?+
180 degrees equals π radians, approximately 3.14159 radians.
What is the difference between degrees and radians?+
Degrees divide a circle into 360 parts. Radians measure angles by the ratio of arc length to radius; a full circle is 2π radians.
Which angle units does this converter support?+
It supports degrees, radians, gradians, arcminutes, arcseconds, turns, milliradians, and compass points.