Convert angles between degrees, radians, gradians, arcminutes, arcseconds, and full turns.
Enter a value to convert.
| Unit | Equals |
|---|---|
| 1 Turn | 360 Degrees |
| 1 Radian | 57.29577951308232 Degrees |
| 1 Degree | 60 Arcminutes |
| 1 Arcminute | 60 Arcseconds |
| 1 Degree | 3,600 Arcseconds |
| 400 Gradians | 360 Degrees |
An angle converter changes a measurement of rotation or angular size from one unit to another while representing the same angle — 90 degrees and about 1.570796 radians describe the same angle, just counted in different units. It's useful for moving between the units used in math, programming, navigation, and engineering.
Degrees and radians are the two most common units for measuring angles. A full circle is 360 degrees, which is the same as 2*pi radians.
Degrees are common in everyday use, navigation, and geometry, while radians are the standard unit in most math and programming contexts — many programming languages' trigonometric functions expect angles in radians rather than degrees.
The gradian (or gon) divides a full circle into 400 equal parts instead of 360. It is used in some surveying and civil engineering contexts. 400 gradians equal 360 degrees, so 100 gradians equal exactly 90 degrees.
Arcminutes and arcseconds subdivide the degree for precise angular measurement. They are used in astronomy, navigation, and surveying, where fine angular resolution matters. 1 degree equals 60 arcminutes, and 1 arcminute equals 60 arcseconds (3,600 arcseconds per degree).
Angle conversions come up in trigonometry and math homework, programming (since many languages use radians in their math functions), navigation and surveying, astronomy, engineering and CAD work, and construction or carpentry where angles are often specified in degrees.
Multiply the number of degrees by pi/180 (approximately 0.0174533), or divide the degree value by 57.29577951308232. For example, 90 degrees equals about 1.570796 radians.
One radian equals approximately 57.2958 degrees (exactly 180/pi degrees).
A gradian (also called a gon) divides a full circle into 400 equal parts instead of 360. It is used in some surveying and engineering contexts. 100 gradians equal 90 degrees, and a full circle is 400 gradians.
There are 60 arcminutes in one degree, and 60 arcseconds in one arcminute (3,600 arcseconds per degree). Arcminutes and arcseconds are used for precise angular measurement in astronomy and navigation.
Yes. A negative angle typically indicates direction or rotation sense — for example, -90 degrees can represent a quarter turn in the clockwise direction rather than counterclockwise. This converter accepts negative values.
A full turn (one complete rotation) equals 360 degrees, which is the same as 2*pi radians or 400 gradians.
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