Angle Units
Convert between degrees, radians, gradians, arcminutes, and arcseconds.
Scientific & Engineering
Perfect for trigonometry, navigation, surveying, and CAD applications.
Accurate Conversions
Precise calculations for mathematics, physics, and engineering work.
Understanding Angle Conversion
Angles measure rotation or the space between two intersecting lines. Degrees (°) are most common in everyday use, with a full circle being 360°. Radians are the standard unit in mathematics and physics, where a full circle equals 2π radians. Gradians (gon) divide a circle into 400 parts, used in some surveying applications.
One radian is the angle subtended by an arc equal in length to the radius. Since a circle's circumference is 2πr, a full circle contains 2π radians. This makes 180° = π radians, a fundamental relationship in trigonometry. Understanding angle conversions is essential for mathematics, engineering, navigation, and computer graphics.
Common Usage Examples
- Mathematics: Trigonometric calculations in radians
- Navigation: Bearing and heading measurements in degrees
- CAD/Design: Rotation angles for 3D modeling
- Surveying: Land measurements using gradians
- Programming: Graphics rotation and animation
- Astronomy: Celestial coordinates and positions
Frequently Asked Questions
How many radians are in a circle?
A full circle contains 2π radians (approximately 6.28 radians). This comes from the circumference formula 2πr, where the radius equals 1.
How do I convert degrees to radians?
Multiply degrees by π/180. For example, 90° × (π/180) = π/2 radians ≈ 1.571 radians. This is essential for trigonometric calculations.
What are gradians used for?
Gradians (gon) are used mainly in surveying and some civil engineering. A right angle is 100 gradians, making calculations decimal-based.
What are arcminutes and arcseconds?
These are subdivisions of degrees. 1 degree = 60 arcminutes = 3,600 arcseconds. They're used in astronomy, navigation, and precision measurements.