Angle Converter
Convert angles between degrees, radians, gradians and the arcminutes and arcseconds used in astronomy and surveying.
Angle Converter
Convert between 7 angle units.
1 Degree = 0.017453293 Radian
1 ° equals
0.017453293 rad
In every unit
Angle units in practice
Drawings, protractors and machine heads use degrees, while maths, programming and engineering formulas use radians. Surveyors in some countries use gradians, where a right angle is 100 gon.
Arcminutes and arcseconds split a degree into 60 and 3,600 parts. They are used for telescope fields of view, map coordinates and the accuracy of precision rotary tables.
Angle unit reference
| Unit | Symbol | In radians |
|---|---|---|
| Degree | ° | 0.017453293 rad |
| Radian | rad | 1 rad |
| Gradian | gon | 0.015707963 rad |
| Arcminute | ′ | 0.00029088821 rad |
| Arcsecond | ″ | 0.000004848137 rad |
| Milliradian | mrad | 0.001 rad |
| Turn | tr | 6.2831853 rad |
Frequently asked questions
How do I convert degrees to radians?
Multiply by π/180, about 0.0174533. So 90° is π/2, about 1.5708 radians.
How do I convert radians to degrees?
Multiply by 180/π, about 57.2958. So 1 radian is about 57.3°.
How many arcseconds are in a degree?
3,600: there are 60 arcminutes in a degree and 60 arcseconds in an arcminute.
What is a gradian?
One 400th of a full turn, so a right angle is 100 gradians. It is also called a gon.