Angle Converter
Convert degrees, radians, gradians and turns.
Convert between angle units used in math, engineering and navigation. Enter a value and pick the units — everything is converted through radians.
Formula / method
Examples
3.1416 rad
360 deg
Degrees, radians, gradians and turns
A full circle can be described four ways: 360 degrees, 2 pi radians, 400 gradians, or 1 turn. That makes one radian about 57.2958 degrees, and one gradian exactly 0.9 degrees. To convert degrees to radians you multiply by pi/180; to go back, multiply radians by 180/pi.
Which unit to use when
Degrees are the everyday choice for navigation, geometry class, and design software. Radians are the native unit of higher math and programming: functions like sin() and cos() in most languages expect radians, so feeding them degrees is a classic bug. Gradians (also called gons) split a right angle into a round 100 units and show up in surveying. Turns are handy when you think in whole rotations, such as 0.25 turn for a quarter circle.
Where it's used
- Converting degrees to radians before calling sin, cos or tan in code, which expect radians
- Surveying work, which is often measured in gradians (gons)
- Converting a navigation heading or bearing between units
- Setting rotation values in CAD or design software
- Expressing part of a full rotation as a fraction of a turn
Real-world examples
- 180 degrees equals pi radians, about 3.1416
- A right angle is 90 degrees, pi/2 radians, or exactly 100 gradians
- A quarter turn (0.25 turn) is 90 degrees
A bit of history
The term 'radian' first appeared in print in 1873, in examination questions set by James Thomson, brother of Lord Kelvin, at Queen's College, Belfast.
FAQ
How many radians are in a circle?
2π ≈ 6.2832 radians make a full circle — the same as 360 degrees or 400 gradians.