💡 360° = 2π rad = 400 grad = 21,600 arcminutes = 1,296,000 arcseconds
📖 How to Use This Angle Converter
1
Enter the value - Type the angle number you want to convert.
2
Select the source unit - Choose from Degrees, Radians, Gradians, Arcminutes, or Arcseconds.
3
Select the target unit - Choose the unit you want to convert to.
4
See instant result - The converted value appears automatically.
📐 Understanding Angular Units
Angles are measured in various units depending on the application. The most common units are degrees and radians, but other units like gradians, arcminutes, and arcseconds are important in specific fields.
- Degrees (°): 1 full circle = 360°. Most common unit for everyday use, navigation, and geography.
- Radians (rad): 1 full circle = 2π rad. The standard unit in mathematics, physics, and engineering.
- Gradians (grad): 1 full circle = 400 grad. Used in surveying and some engineering applications.
- Arcminutes ('): 1° = 60 arcminutes. Used in astronomy, navigation, and precision measurements.
- Arcseconds ("): 1° = 3600 arcseconds. Used in astronomy (stellar positions) and geodesy.
🧮 Conversion Formulas
To Degrees: Radians×180/π | Gradians×0.9 | Arcminutes÷60 | Arcseconds÷3600
From Degrees: Radians×π/180 | Gradians÷0.9 | Arcminutes×60 | Arcseconds×3600
💡 Common Applications
- Astronomy: Arcminutes and arcseconds measure angular distances between stars
- Navigation: Degrees, minutes, seconds used in GPS coordinates
- Trigonometry: Radians are the natural unit for calculus
- Surveying: Gradians simplify right-angle calculations
❓ Frequently Asked Questions
Why do we use radians instead of degrees?
Radians are the natural unit for angle measurement in calculus and physics because they simplify derivatives and integrals of trigonometric functions.
What is the difference between arcminutes and minutes of time?
Arcminutes (') measure angle (1° = 60 arcminutes). Minutes of time measure time (1 hour = 60 minutes).
What is 1 radian in degrees?
1 radian = 180/π degrees ≈ 57.2957795°.
What are gradians used for?
Gradians are primarily used in surveying and some engineering applications.
How many arcseconds are in a degree?
There are 3,600 arcseconds in one degree.