Angle Unit Converter
Angle measures the rotational offset between two lines. While we intuitively use Degrees (360° in a circle), advanced mathematics, calculus, and physics rely on Radians, while some surveying systems utilize Gradians.
This professional angle calculator provides instant, high-precision translation between these systems. It also handles the sexagesimal units used in astronomy and GPS navigation, converting Arcminutes and Arcseconds with extreme accuracy.
Primary Units
GeometrySubdivisions
PrecisionCommon Conversion Factors
1 Radian ≈ 57.2958°
1 Degree = 0.01745 Radians
1 Gradian = 0.9°
1 Degree = 60′ (Arcminutes)
Angle Units Explained
- Radian (rad): The standard unit of angular measure in mathematics (Calculus). One radian is the angle at the center of a circle subtended by an arc equal in length to the radius. A full circle is 2π radians.
- Gradian (gon): Also known as the grad, this unit divides a right angle into 100 parts rather than 90. It is primarily used in surveying and mining.
- DMS (Degrees, Minutes, Seconds): Used in navigation and astronomy. A degree is divided into 60 arcminutes, and an arcminute into 60 arcseconds.
Frequently Asked Questions
To convert degrees to radians, multiply the degree value by π/180. For example, 180° × (π/180) = π radians (approx 3.14159).
A Gradian (or Gon) is a unit of angle where a right angle equals 100 gradians. A full circle is 400 gradians. It simplifies right-angle calculations in surveying.
There are exactly 60 Arcminutes in 1 Degree. Consequently, there are 3,600 Arcseconds in 1 Degree.
How to Use This Converter
Convert angles for geometry, navigation, and surveying in 3 steps.
Input Value
Type your known angle into the corresponding field (e.g., enter “180” in the Degree field).
View Conversions
The calculator automatically generates equivalent values in Radians, Gradians, Arcminutes, and Arcseconds.
Copy Data
Click the copy icon next to any field to save the precise result to your clipboard for use in other applications.