Angle Converter
Convert degrees, radians, gradians, and arc minutes.
Enter a value, choose the units, and see the result plus every other angle unit.
Degree → Radian
Angle Converter
Convert angles between degrees, radians, gradians, arc minutes and arc seconds, turns, milliradians, NATO mils, and quadrants. It is built for math homework, programming with trigonometric functions, surveying, navigation, and shooting optics.
How the units relate
Every unit is defined as a fraction of a full circle:
| Unit | Per full circle | One unit in degrees |
|---|---|---|
| Turn | 1 | 360 |
| Quadrant | 4 | 90 |
| Gradian (gon) | 400 | 0.9 |
| Degree | 360 | 1 |
| NATO mil | 6,400 | 0.05625 |
| Radian | 2π ≈ 6.2832 | 57.2958 |
A degree splits into 60 arc minutes, and each arc minute into 60 arc seconds, so 1° = 3,600″.
Radians in programming
JavaScript, Python, C, and most other languages expect radians in sin(), cos(), and tan(). Passing 30 directly gives the sine of 30 radians, not 30 degrees. Convert first: 30° = 0.523599 rad, and Math.sin(0.523599) returns 0.5 as expected. Likewise, 90° is π/2 and 180° is exactly π.
Maps, astronomy, and GPS
Coordinates are often written in degrees and minutes. A latitude reading of 12.5° is 750 arc minutes, and half a degree is 30′. Astronomers measure tiny angles in arc seconds: 1″ is only 4.848e-6 rad, about the size of a coin seen from several kilometers away.
Surveying and military units
Surveyors in parts of Europe use gradians because a right angle is a round 100 gon. Artillery and compasses use the NATO mil (6,400 per circle, so 1° ≈ 17.78 mil), while rifle scopes use the milliradian, where 1 mrad covers 10 cm at 100 m.
For rotation speeds such as degrees per second or rpm, open the Frequency Converter. Degree values in CSS color hues can be explored with HEX to HSV.
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180. For example, 180° × π/180 = π ≈ 3.14159 rad, and 45° is π/4 ≈ 0.785398 rad. To go back, multiply radians by 180/π (about 57.2958).
What is a gradian?
A gradian (gon) divides a right angle into 100 parts, so a full circle is 400 gon. It is used in surveying and in some European civil engineering.
What is the difference between a milliradian and a NATO mil?
A milliradian is exactly 1/1000 rad, about 0.0573°. The NATO mil divides a circle into 6,400 parts, making it 0.05625°. The two are close but not interchangeable when aiming or reading a compass.