Quick example
Convert 180 degrees to radians
A complete turn is 360 degrees or 2π radians. Half a turn is therefore 180 degrees or exactly π radians, approximately 3.14159265359 radians.
Quick reference
Common angle conversions
| Starting angle | Equivalent |
|---|---|
| 1 turn | 360° |
| 1 turn | 2π rad |
| 1 turn | 400 gon |
| 180° | π rad |
| 90° | 100 gon |
| 1 rad | 57.29577951° |
| 1° | 60 arcmin |
| 1° | 3,600 arcsec |
Unit definitions
Turns, radians, degrees, and subdivisions
Degrees
Degrees divide one complete turn into 360 equal parts. A right angle is 90 degrees.
Radians
Radians relate arc length to radius. One complete turn is exactly 2π radians.
Gradians and turns
Gradians divide a turn into 400 parts, making a right angle 100 gon. A turn directly counts complete rotations.
Arcminutes and arcseconds
One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds. They measure angle, not time.
Rotation scope
Angles are converted, not normalized
This tool preserves the value's full rotation information. For example, 720° converts to 2 turns rather than 0°, and −90° converts to −0.25 turn. Whether equivalent directions should be wrapped into a particular range depends on the application.
Common questions
Angle conversion FAQ
How many radians are in 180 degrees?
180 degrees equals exactly π radians, approximately 3.14159265359 radians.
How do I convert radians to degrees?
Multiply radians by 180 divided by π. For example, π/2 radians equals 90 degrees.
How many degrees, radians, and gradians are in one turn?
One turn equals 360 degrees, 2π radians, and 400 gradians.
How many arcminutes and arcseconds are in one degree?
One degree contains exactly 60 arcminutes or 3,600 arcseconds.
Can angles be negative or greater than 360 degrees?
Yes. This converter preserves negative angles and multiple turns rather than wrapping them.