Angle Unit Converter
The angle unit converter allows you to convert between commonly used angle measurements such as degrees, radians, and gradians. This tool is useful for mathematicians, engineers, physicists, navigators, and anyone working with angular measurements. Select a conversion below or choose from popular angle unit conversions.
Supported Angle Units
| Unit | Short Form | Description |
|---|---|---|
| Radian | rad | SI unit of angular measurement, arc length equals radius |
| Degree | deg | 1/360 of a full circle |
| Gradian | grad | 1/400 of a full circle, also called gon |
| Cycle | cycle | One complete rotation, equal to 360 degrees |
| Arcsecond | arcsec | 1/3600 of a degree |
| Arcminute | arcmin | 1/60 of a degree |
Popular Angle Conversions
- Degree to Radian
- Radian to Degree
- Degree to Gradian
- Gradian to Degree
- Arcminute to Degree
- Degree to Arcminute
How Angle Unit Conversion Works
Angle units are converted using fixed mathematical ratios based on circle divisions.
For example, 1 radian equals approximately 57.2958 degrees, and 1 degree equals π/180 radians.
Our angle converter uses accurate conversion factors to ensure precise results for trigonometry, navigation, and engineering calculations.
Common Use Cases
- Trigonometric calculations
- Navigation and surveying
- Engineering and CAD design
- Astronomy and celestial measurements
- Physics and rotational mechanics
Frequently Asked Questions
How accurate is the angle unit converter?
Our converter uses precise conversion factors including the exact value of π. Results are accurate to multiple decimal places, making it suitable for professional use in mathematics, engineering, and scientific applications.
What’s the difference between degrees and radians?
Degrees divide a circle into 360 equal parts, a traditional and intuitive system. Radians are based on the radius of a circle - one radian is the angle where the arc length equals the radius. Radians are preferred in calculus and advanced mathematics because they simplify many formulas.
How many radians are in a circle?
A full circle contains exactly 2π radians, which equals approximately 6.28318 radians. This is equivalent to 360 degrees.
How many degrees are in a radian?
1 radian equals approximately 57.2958 degrees. To convert radians to degrees, multiply by 180/π.
What is a gradian?
A gradian (also called a gon) divides a circle into 400 equal parts, making a right angle equal to 100 gradians. It was designed to simplify calculations in surveying but is less common than degrees or radians.
How do I convert degrees to radians?
To convert degrees to radians, multiply by π/180. For example, 90 degrees equals π/2 radians (approximately 1.5708 radians).
What are arcminutes and arcseconds?
Arcminutes and arcseconds are subdivisions of degrees used in astronomy, navigation, and surveying. 1 degree = 60 arcminutes = 3,600 arcseconds. They allow for very precise angular measurements.