Angle Converter (Degrees, Radians, Gradians)
Enter an angle, then choose what it is in and what you want it in.
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Formula
Every unit is a fixed fraction of a full turn: 1 turn = 360° = 2π rad = 400 gon = 21,600′ = 1,296,000″ = 6,400 NATO mils.
radians = degrees × π ÷ 180degrees = radians × 180 ÷ πgradians = degrees × 10 ÷ 9
Worked example
| From | To | Calculation | Result |
|---|---|---|---|
| 180° | rad | 180 × π ÷ 180 | 3.141593 |
| 45° | rad | 45 × π ÷ 180 | 0.785398 |
| 1 rad | ° | 180 ÷ π | 57.29578 |
| 90° | gon | 90 × 10 ÷ 9 | 100 |
| 0.25 turn | ° | 0.25 × 360 | 90 |
| 1° | ″ | 60 × 60 | 3600 |
Frequently asked questions
How do I convert degrees to radians?
Multiply the degrees by π and divide by 180. For 180° that gives π, or 3.141593 radians; for 45° it is 0.785398 radians.
How many degrees are in a radian?
One radian is 180 ÷ π degrees, which is 57.29578°. A full turn is 2π radians, or 360°.
What is a gradian?
A gradian (gon) is 1/400 of a turn, so a right angle is exactly 100 gradians and 90° equals 100 gon.
How many arcseconds are in a degree?
A degree has 60 arcminutes and each arcminute has 60 arcseconds, so one degree is 3,600 arcseconds. One arcsecond is about 0.000278°.