Angle Converter
Plane angle - degrees, radians, gradians.
Enter a value above to convert between ° and rad.
How to convert angle units
Angle is based on the degree. A full circle is 360° = 2π radians = 400 gradians. Radians relate by radians = degrees × π/180 and degrees = radians × 180/π, so one radian is about 57.29578°.
Worked example
Ninety degrees is 90 × π/180 = 1.5708 rad (π/2). One radian is 57.29578°. A right angle is 100 gradians, and a full turn is 360° = 400 gradians.
How many degrees are in a radian?
One radian equals 57.29577951°. A full turn equals 360° = 2π radians = 400 gradians. One gradian equals 0.9°, one arcminute is 1/60 of a degree, and one arcsecond is 1/3600 of a degree.
When you'll use an angle converter
Angle conversion is useful in math and trigonometry (degrees versus radians), engineering and CAD, surveying (gradians, arcminutes, arcseconds), and navigation. The table above lists your value in all 6 supported units at once.
Common angle conversions
Quick-reference rates for common angle conversions - degrees, radians, gradians, arcminutes and turns, one unit at a time.
| From | To |
|---|---|
| 1 degree (°) | 0.0175 rad |
| 1 radian (rad) | 57.2958 ° |
| 1 turn (turn) | 360 ° |
| 1 degree (°) | 1.1111 grad |
| 1 gradian (grad) | 0.9 ° |
| 1 turn (turn) | 6.2832 rad |
| 1 radian (rad) | 0.1592 turn |
| 1 radian (rad) | 63.662 grad |
| 1 degree (°) | 60 ′ |
| 1 turn (turn) | 400 grad |
Frequently asked questions
How many arcseconds are in a degree?
There are 3,600 arcseconds in one degree, because a degree is divided into 60 arcminutes and each arcminute holds 60 arcseconds. So one arcsecond equals 1/3600 of a degree.
Is a radian bigger than a degree?
Yes, a radian is much larger than a degree. One radian equals about 57.29578 degrees, so a single radian spans more than 57 full degrees of arc.
How do I convert gradians to degrees?
Multiply the number of gradians by 0.9 to get degrees, since one gradian equals 0.9 degrees. For example, 50 gradians is 50 times 0.9, which equals 45 degrees.
What is a turn in angle measurement?
A turn is one complete rotation, equal to 360 degrees, 2 pi radians, or 400 gradians. It is a handy unit for describing full revolutions in rotation and motion.
How many arcseconds are in an arcminute?
There are 60 arcseconds in one arcminute. Both are fine subdivisions of a degree used in surveying, astronomy, and precise navigation.
What is 45 degrees in radians?
45 degrees equals about 0.7853982 radians, which is pi divided by 4. You get it by multiplying 45 by pi and dividing by 180.
Popular angle conversions
Quick links to popular angle conversions - tap any pair to open the converter ready to go.