Units
Angle converter
Degrees to radians, gradians, arcminutes and arcseconds. For trigonometry, surveying and programming.
Conversions are worked out on your own machine. No sign-up, no waiting and nothing sent anywhere.
Common conversions
| degree | radian |
|---|---|
| 1 ° | 0.017453 rad |
| 15 ° | 0.261799 rad |
| 30 ° | 0.523599 rad |
| 45 ° | 0.785398 rad |
| 60 ° | 1.0472 rad |
| 90 ° | 1.5708 rad |
| 180 ° | 3.1416 rad |
| radian | degree |
|---|---|
| 1 rad | 57.296 ° |
| 15 rad | 859.437 ° |
| 30 rad | 1,718.87 ° |
| 45 rad | 2,578.31 ° |
| 60 rad | 3,437.75 ° |
| 90 rad | 5,156.62 ° |
| 180 rad | 10,313.24 ° |
| degree | gradian |
|---|---|
| 1 ° | 1.1111 gon |
| 15 ° | 16.667 gon |
| 30 ° | 33.333 gon |
| 45 ° | 50 gon |
| 60 ° | 66.667 gon |
| 90 ° | 100 gon |
| 180 ° | 200 gon |
| turn | degree |
|---|---|
| 1 turn | 360 ° |
| 15 turn | 5,400 ° |
| 30 turn | 10,800 ° |
| 45 turn | 16,200 ° |
| 60 turn | 21,600 ° |
| 90 turn | 32,400 ° |
| 180 turn | 64,800 ° |
Worked out with the same factors the converter above uses.
The degree divides the circle into 360 parts, a Babylonian inheritance that survives because 360 has so many divisors: it splits cleanly into 2, 3, 4, 5, 6, 8, 9, 10, 12 and more. Convenient for drawing and for talking.
The radian is mathematics' natural unit: the angle whose arc equals the radius. A full circle is 2π radians, so 180° is π radians and one radian is about 57.3°. It matters because almost every programming language expects radians: in JavaScript, Python or C, sin(90) does not give 1, it gives 0.894, because it reads 90 as radians. Converting first is not optional.
The gradian divides the circle into 400 parts, making a right angle exactly 100 gon. It was invented alongside the metric system and survives in surveying because it makes gradient arithmetic tidier. And astronomy and navigation still split the degree into 60 arcminutes and each minute into 60 arcseconds, just like hours.
Every unit in this category
Frequently asked questions
How many radians is 180 degrees?
π radians, about 3.1416. And 360° is 2π. The formula is rad = degrees × π/180.
Why is my calculator giving the wrong sine?
Almost certainly because it is in the wrong mode. Most languages and many calculators work in radians by default: sin(90) in radians is 0.894, not 1. Convert degrees to radians first.
What is the gradian for?
Mostly surveying: with 100 gon in a right angle, gradient percentages and subdivisions come out without awkward decimals. Outside that it is barely used.