Angle Converter
Enter a value and select units to convert
Enter a value and select units to convert
The angle converter allows you to convert between different angular measurement units like degrees, radians, gradians, and more. This tool is useful for mathematics, engineering, navigation, astronomy, and many other fields where precise angular measurements are needed.
Common Angle Measurement Systems
Degree-Based Systems
The degree is one of the most common units for measuring angles, especially in everyday applications.
- Degree (°): 1/360 of a full rotation
- Minute of arc (′): 1/60 of a degree
- Second of arc (″): 1/60 of a minute of arc or 1/3600 of a degree
Radian-Based Systems
The radian is the SI unit for measuring angles and is commonly used in mathematics and physics.
- Radian (rad): The angle subtended at the center of a circle by an arc equal in length to the radius
- Milliradian (mrad): 1/1000 of a radian, commonly used in military applications
- A full circle is 2π radians (approximately 6.28318 radians)
Other Angular Measurement Systems
Various other systems exist for specific applications.
- Gradian (grad): 1/400 of a full rotation, used in some European countries
- Turn/Revolution/Circle: A complete 360° rotation
- Mil: Used in military applications for artillery and targeting
- NATO mil: 1/6400 of a full circle (0.05625°)
- Russian mil: 1/6000 of a full circle (0.06°)
- Compass points: Used in navigation, dividing a full circle into 32 points
Geometric References
Certain angles are referenced by their geometric significance.
- Right angle: 90° or π/2 radians
- Quadrant: 1/4 of a full circle (90°)
- Sextant: 1/6 of a full circle (60°)
Common Angle Conversions
| From | To | Multiply By |
|---|---|---|
| Degrees | Radians | π/180 (≈ 0.01745) |
| Radians | Degrees | 180/π (≈ 57.2958) |
| Degrees | Gradians | 10/9 (≈ 1.1111) |
| Gradians | Degrees | 9/10 (= 0.9) |
| Degrees | Minutes of arc | 60 |
| Minutes of arc | Seconds of arc | 60 |
| Degrees | Turns | 1/360 (≈ 0.002778) |
| Turns | Degrees | 360 |
| Radians | Milliradians | 1000 |
| Degrees | NATO Mils | 17.7778 |
| Degrees | Russian Mils | 16.6667 |