Angle Converter
Convert between various units of angle, including degrees, radians, gradians, minutes of arc, and seconds of arc.
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About Angle Units
An angle is the figure formed by two rays sharing a common endpoint (vertex). Angular measurement quantifies the amount of rotation needed to bring one ray to the position of the other.
Common Angle Units
- Degree (°): One of the oldest and most common units. A full circle is divided into 360 degrees. One degree is 1/360 of a full rotation.
- Radian (rad): The SI unit of angle measurement. A full circle is 2π radians (approximately 6.28318 radians). One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
- Gradian (grad): Also called a gon, this unit divides a full circle into 400 gradians. One gradian is 1/400 of a full rotation, making 90° equal to 100 gradians.
- Minute of arc ('): A subdivision of a degree. One degree equals 60 minutes of arc. Often used in astronomy, navigation, and angular precision measurements.
- Second of arc ("): A further subdivision of angular measurement. One minute of arc equals 60 seconds of arc. Used in high-precision applications like astronomy.
Angle Conversion Applications
Angle conversions are essential in numerous fields:
- Mathematics and trigonometry calculations
- Engineering and construction for structural design
- Navigation and mapping for directions and positioning
- Astronomy for celestial body positions and movements
- Physics for vector calculations and wave properties
- Computer graphics and game development for rotations and orientations
- Surveying and land measurement
Important Angle Relationships
Understanding these relationships helps with conversions:
- A full circle = 360 degrees = 2π radians = 400 gradians
- 1 degree = π/180 radians ≈ 0.01745 radians
- 1 radian = 180/π degrees ≈ 57.2958 degrees
- 1 degree = 60 minutes of arc
- 1 minute of arc = 60 seconds of arc
- 1 degree = 10/9 gradians
- 1 gradian = 0.9 degrees