1 rad in every unit
Values update with the converter above. Select a row to open that conversion's detailed page.
- Degree57.29578 °
- Gradian63.66198 gon
- Full Turn0.1591549 tur
Popular conversions
3 pairsDegree ↔ Radian
° ↔ rad
Degree ↔ Gradian
° ↔ gon
Degree ↔ Full Turn
° ↔ tur
Unit guides
4 unitsDetailed guide to this category
Angle measures the amount of rotation between two rays sharing a common endpoint.
The radian is the SI unit of angle, while the degree is the most common practical unit for everyday and navigational use.
- Physical quantity
- Angle
- SI unit
- Radian
- Common practical unit
- Degree
- Typical use
- Trigonometry, navigation and engineering drawing
What is angle?
Angle is the amount of rotation between two rays sharing a common endpoint, measured in degrees, radians or gradians.
It is used in trigonometry, geometry, navigation and engineering.
Degrees, radians and gradians
A full circle is 360 degrees, 2π radians, or 400 gradians. The degree traces back to ancient Babylonian base-60 mathematics, while the radian is the natural SI unit for mathematical calculations.
Choosing an angle unit
Degrees are common in everyday measurement, surveying and navigation. Radians are normally used in trigonometry, calculus and many engineering formulas because they relate an angle directly to an arc length and radius.
Gradians divide a full turn into 400 parts and appear in some surveying and technical contexts. A full turn is useful when rotations are counted rather than expressed as a partial circle.
How angle units are converted
Angle conversions preserve the same rotation. Use a fixed full-circle relationship: 360 degrees equals 2π radians, 400 gradians and one full turn.
Keep the unit explicit when entering values into calculators or engineering software, because trigonometric functions may expect radians by default.
Unit comparison table
| Unit | Symbol | SI equivalent | System | Common use |
|---|---|---|---|---|
| Radian | rad | 2π rad = 1 full turn | SI coherent derived unit | Mathematics, physics and engineering |
| Degree | ° | 360° = 1 full turn | Practical angular measure | Navigation, geometry and daily measurement |
| Gradian | gon | 400 gon = 1 full turn | Metric angular measure | Surveying and technical drawing |
| Full Turn | turn | 1 turn = 360° | Rotation count | Rotating machinery and motion |
Units
| Unit | Symbol | Information |
|---|---|---|
| Radian | rad | View unit guide |
| Degree | ° | View unit guide |
| Gradian | gon | View unit guide |
| Full Turn | turn | View unit guide |