Angles Converter
Convert between degrees, radians, gradians, arcminutes, arcseconds, turns, military mils and other units of angle.
1 radian = 1 radian
Most used angle units
- Degree ° 1 ° = 0.017453293 rad
- Radian rad Base unit
- Arcminute ′ 1 ′ = 0.00029088821 rad
- Arcsecond ″ 1 ″ = 0.000004848137 rad
- Gradian grad 1 grad = 0.015707963 rad
- Milliradian mrad 1 mrad = 0.001 rad
- Turn tr 1 tr = 6.2831853 rad
- NATO mil mil 1 mil = 0.0009817477 rad
- Milliarcsecond mas 1 mas = 4.8481368 × 10-9 rad
- Compass point 1 compass point = 0.19634954 rad
- Hour angle h 1 h = 0.26179939 rad
- Microradian µrad 1 µrad = 0.000001 rad
Popular angle conversions
- Degrees to radians 1 ° = 0.01745329 rad
- Radians to degrees 1 rad = 57.29578 °
- Degrees to gradians 1 ° = 1.111111 grad
- Gradians to degrees 1 grad = 0.9 °
- Degrees to arcminutes 1 ° = 60 ′
- Arcseconds to degrees 1 ″ = 0.0002777778 °
- Degrees to NATO mils 1 ° = 17.77778 mil
- Turns to degrees 1 tr = 360 °
- Milliradians to degrees 1 mrad = 0.05729578 °
- Degrees to milliradians 1 ° = 17.45329 mrad
- Radians to turns 1 rad = 0.1591549 tr
- Arcminutes to degrees 1 ′ = 0.01666667 °
What is angle?
An angle measures the amount of turn between two lines that meet at a point. The most familiar unit is the degree: a full circle is 360°, a right angle 90°. Mathematicians and physicists prefer the radian, the angle at which the arc of a circle equals its radius; a full circle is 2π radians, about 6.283.
Other units divide the circle differently: the gradian (400 per circle) was designed for decimal surveying, the military mil (6,400 per circle in NATO) makes range estimation easy, and navigators once used the 32 points of the compass. Astronomers measure tiny angles in arcminutes and arcseconds, 1/60 and 1/3,600 of a degree.
Degrees and radians
- Radians to degrees: degrees = radians × 180/π (1 rad ≈ 57.2958°)
- Degrees to radians: radians = degrees × π/180 (1° ≈ 0.0174533 rad)
- Common angles: 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2, 180° = π, 360° = 2π
- 1 degree = 60 arcminutes = 3,600 arcseconds
Angle units from smallest to largest
Every proportional angle unit on the site, ordered by size and expressed in radians.
- Microarcsecond 4.848137 × 10-12 rad
- Milliarcsecond 4.848137 × 10-9 rad
- Microradian 0.000001 rad
- Arcsecond 0.00000484814 rad
- Second of time 0.0000727221 rad
- Arcminute 0.000290888 rad
- NATO mil 0.000981748 rad
- Swedish streck 0.000997331 rad
- Milliradian 0.001 rad
- Warsaw Pact mil 0.0010472 rad
- Minute of time 0.00436332 rad
- Gradian 0.015708 rad
- Degree 0.0174533 rad
- Binary degree 0.0245437 rad
- Quarter point 0.0490874 rad
- Hexacontade 0.10472 rad
- Compass point 0.19635 rad
- Hour angle 0.261799 rad
- Zodiac sign 0.523599 rad
- Octant 0.785398 rad
- Radian 1 rad
- Sextant 1.0472 rad
- Quadrant 1.5708 rad
- Turn 6.28319 rad
All 24 angle units
Common
Astronomy & precision
Traditional & military
Frequently asked questions
How many degrees are in a radian?
One radian is 180/π degrees, about 57.2958°.
Why are there 360 degrees in a circle?
The number goes back to Babylonian astronomy. 360 is close to the number of days in a year and divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12 and more.
What is a mil?
An angular mil divides a circle into 6,400 parts (NATO). At 1 km, 1 mil subtends about 1 m, which makes range and adjustment calculations easy.