Angle Conversion - Convert Degrees, Radians, Gradians, and More
Understanding Angle Measurements
Angle measurement is fundamental in geometry, navigation, and various technical fields. The radian (rad) is the base unit of angle in the International System of Units (SI), while degrees (°) and gradians (grad) are commonly used in different applications. Understanding angle conversions is essential for mathematics, engineering, and navigation.
Common Angle Units
SI Units
- Radian (rad) - Base unit
- Milliradian (mrad) - 1/1000 of a radian
- Degree (°) - π/180 radians
- Minute (') - 1/60 of a degree
Other Units
- Gradian (grad) - 400 gradians = 360°
- Second ('') - 1/60 of a minute
- Turn (rev) - 360° or 2π radians
- Quadrant - 90° or π/2 radians
Common Applications
| Field | Common Units | Typical Uses |
|---|---|---|
| Mathematics | Radians, degrees | Trigonometry, calculus |
| Navigation | Degrees, minutes | Compass bearings, GPS |
| Engineering | Degrees, radians | Mechanical design, CAD |
| Astronomy | Degrees, arcminutes | Celestial coordinates |
Conversion Tips
- 1 radian equals approximately 57.2958 degrees
- 1 degree equals π/180 radians
- 1 gradian equals 0.9 degrees
- Remember that angles can be positive or negative
Angle Conversions
| Conversion | Formula | Quick Answer |
|---|---|---|
| degree to radian | 1° = π/180 radians | Multiply degrees by 0.0174533 |
| radian to degree | 1 rad = 180/π degrees | Multiply radians by 57.2958 |
| degree to gradian | 1° = 1.11111 gradians | Multiply degrees by 1.11111 |
| gradian to degree | 1 grad = 0.9 degrees | Multiply gradians by 0.9 |
| degree to minute | 1° = 60 arcminutes | Multiply degrees by 60 |
| minute to degree | 1 arcminute = 0.0166667 degrees | Divide arcminutes by 60 |
| degree to second | 1° = 3600 arcseconds | Multiply degrees by 3600 |
| second to degree | 1 arcsecond = 0.000277778 degrees | Divide arcseconds by 3600 |
| radian to gradian | 1 rad = 63.662 gradians | Multiply radians by 63.662 |
| gradian to radian | 1 grad = 0.01570796 radians | Multiply gradians by 0.01570796 |
Our angle conversion tool provides accurate conversions between all common units of angle measurement, making it easy to switch between different systems. Whether you're working in mathematics, navigation, or engineering, our converter ensures precise angle conversions for any application.
Angle Conversion Questions
Everything you need to know about angle measurements and conversions
Have more questions? Our conversion tools are designed to be accurate and user-friendly.