Convert between degrees, radians, and gradians
The angle converter is a specialized mathematical tool for converting between the three main units of angle measurement: degrees (°), radians (rad), and gradians (gon). Essential for math students, physicists, engineers, surveyors, 3D graphics developers, CAD designers, and professionals working with trigonometry, navigation, astronomy, mechanical design, or any field requiring precise angle calculations in different measurement systems.
The tool applies standard mathematical relationships between different angular units:
Enter the angle value you want to convert in the numeric input field.
Select the source angular unit (degree, radian, or gradian) from the 'From' selector.
Choose the target unit in the 'To' selector and the conversion is calculated instantly.
Use the result in your trigonometric calculations, technical designs, or graphics programming.
This tool is fundamental in multiple scientific and technical disciplines:
Students solving trigonometry problems who need to convert between degrees and radians to use trigonometric functions.
Video game and 3D graphics developers working with rotations who need conversions between different angular systems.
Engineers and surveyors performing land measurements who must convert angles between systems according to regional standards.
Astronomers and navigators calculating celestial positions who need precision in angular measurements.
Remember: 360° = 2π radians = 400 gradians. A full circle always equals these amounts.
Radians are the 'natural' unit in mathematics. The functions sin(), cos(), tan() in programming expect radians, not degrees.
To quickly convert degrees to radians: multiply by π/180. For radians to degrees: multiply by 180/π.
Radians are the 'natural' unit because they directly relate the angle to arc length. 1 radian is the angle whose arc measures exactly 1 radius. They simplify many mathematical formulas.
Gradians (or gon) divide the circle into 400 parts. They're mainly used in surveying and some European countries because 100 gradians = right angle, facilitating decimal calculations.
45° × π/180 = π/4 radians ≈ 0.785 radians. This is one-eighth of a circle. Memorize common conversions: 90° = π/2, 180° = π, 270° = 3π/2, 360° = 2π.