About This Radians to Degrees Converter
The radian (rad) is the SI unit of angle, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One full rotation is 2π radians (approximately 6.2832 rad). Radians are the natural unit for mathematical formulas — trigonometric functions in programming and calculus use radians by default. The degree (°) divides a full rotation into 360 equal parts, making it the unit most people use for everyday angles, navigation, and engineering drawings.
This converter handles four angle units — radians, degrees, gradians, and turns. Mathematics and physics students checking trigonometry results, robotics and animation engineers converting between sensor outputs and display values, and graphics programmers using CSS rotations (degrees) alongside canvas or WebGL transforms (radians) all reach for this converter regularly.
How to Use This Converter
- Enter your angle value in the Value field.
- Select the unit you are converting from (e.g., Radian) in the From selector.
- Select the unit you want in the To selector (e.g., Degree).
- The result and formula appear instantly below the inputs.
- Use Swap to reverse the direction, or Reset to clear all fields.
Units Covered
| Unit | Symbol | Common Use |
|---|---|---|
| Radian | rad | Mathematics, physics, programming — natural unit for trig functions |
| Degree | deg | Navigation, engineering drawings, everyday angle measurement (360° = full circle) |
| Gradian | grad | Surveying and some European engineering (400 grad = full circle) |
| Turn | turn | Animation and CSS: 1 turn = 360° = 2π rad = 400 grad |
Radians to Degrees Conversion Table
| Radians [rad] | Degrees [°] |
|---|---|
| 0 rad | 0° |
| 0.5236 (π/6) rad | 30° |
| 0.7854 (π/4) rad | 45° |
| 1.0472 (π/3) rad | 60° |
| 1.5708 (π/2) rad | 90° |
| 2.0944 (2π/3) rad | 120° |
| 3.1416 (π) rad | 180° |
| 4.7124 (3π/2) rad | 270° |
| 5.2360 (5π/3) rad | 300° |
| 6.2832 (2π) rad | 360° |
How to Convert Radians to Degrees
To convert radians to degrees, multiply by 180/π (approximately 57.2958):
Example: Convert π/3 rad to degrees:
To convert degrees back to radians, multiply by π/180 (approximately 0.017453):
Example: Convert 90° to radians:
When You Need to Convert Radians to Degrees
Programming is the most common professional context. JavaScript, Python, C, and most other languages pass angles to trigonometric functions (sin, cos, tan) in radians. A developer working with a rotation input field that accepts degrees — say, a CSS transform where the user types 45 — must convert to radians before passing the value to a math function: 45° = π/4 ≈ 0.7854 rad. Getting this wrong produces silent calculation errors that are hard to trace.
Physics and engineering coursework requires switching between both systems. Textbooks define angular velocity in radians per second (rad/s), angular acceleration in rad/s², and arc length formulas using radians. But navigation and compass work uses degrees. A student calculating the arc length of a 45° sector of a 10 m radius circle needs to convert 45° to π/4 rad first: arc = 10 × π/4 = 7.854 m.
3D animation and robotics also mix both units. Rigging systems in tools like Blender or Maya display joint rotations in degrees for the artist, while the underlying engine stores and computes in radians. Robot arm joint controllers may receive degree commands from a user interface but need to convert to radians for motor drive calculations. This converter handles the full set of angle units — including gradians, which appear in European surveying instruments and some CAD software.