Angle Converter
Convert Degrees, Radians, and Gradians.
📐 Angle Converter
What is Angle Converter?
Angle Converter converts angle values between three main units: degrees (°), radians (rad), and gradians (gon). One full circle = 360° = 2π radians = 400 gradians. Radians are the standard unit in mathematics and programming (JavaScript, Python, and PHP trigonometric functions all use radians), while degrees are more common in everyday life, and gradians are used in surveying and military fields.
How Does It Work?
The tool first converts the input value to radians as an intermediate unit, then converts from radians to degrees and gradians. The formulas are: radians = degrees × π/180, and gradians = degrees × 10/9. The tool displays all three results at once so you can see the value in every unit without needing to calculate manually.
Common Use Cases
- Programming - JavaScript's Math.sin() function uses radians, so converting from degrees is very often needed.
- Mathematics & physics - Trigonometry and calculus problems usually use radians, while geometry problems use degrees.
- Surveying & construction - Gradians (gon) are used in land surveying and building angle calculations.
- Game development - Object rotation in game engines is often in degrees, but internal calculations use radians.
- Navigation & astronomy - Coordinates and bearings use degrees, so quick conversion is very helpful.
Frequently Asked Questions
Q: Why is 180° = π radians?
A: Because one full circle is 360° = 2π radians. So half a circle (180°) = π radians. This is the basic definition of a radian: arc length divided by radius.
Q: What is a gradian and when is it used?
A: A gradian (gon) divides a circle into 400 parts. One gradian = 0.9°. It's used in European surveying, construction, and some military applications because it simplifies right-angle calculations (100 gon = 90°).
Q: Which unit should I use on a calculator?
A: It depends on the context. Scientific calculators usually have DEG/RAD/GRAD modes. For advanced mathematics and programming, use radians. For everyday life and basic geometry, use degrees.