Angle Converter
Convert between various units of angle, including degrees, radians, gradians, minutes of arc, and seconds of arc.
How to Convert Degrees to Radians
Multiply the number of degrees by π/180 to get radians.
radians = degrees × π/180
Example: 90° × π/180 = 1.5708 radians
How to Convert Radians to Degrees
Multiply the number of radians by 180/π to get degrees.
degrees = radians × 180/π
Example: 2 radians × 180/π = 114.592°
How to Convert Gradians to Degrees
Multiply the number of gradians by 0.9 to get degrees.
degrees = gradians × 0.9
Example: 100 gradians × 0.9 = 90°
Angle Conversion FAQs
- How do you convert degrees to radians?
- What is the formula for radians to degrees?
- How do you convert gradians to degrees?
- What is angle conversion?
- How many radians are in a degree?
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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