Angle Converter — Degrees, Radians, Gradians, Turns
Convert angles between degrees, radians, gradians, and turns instantly with real-time results.
Common angles:
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Result
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Formula
Angle Unit Reference
| Unit | Full Circle | Right Angle | Used In |
|---|---|---|---|
| Degree (°) | 360° | 90° | Everyday geometry, navigation |
| Radian (rad) | 2π ≈ 6.2832 | π/2 ≈ 1.5708 | Mathematics, physics |
| Gradian (grad) | 400 grad | 100 grad | Surveying, civil engineering |
| Turn | 1 turn | 0.25 turn | Programming, rotations |
Frequently Asked Questions
How do I convert degrees to radians?
Multiply degrees by π/180 (≈ 0.017453). For example, 180° = π radians ≈ 3.14159 rad. Radians are the SI unit for angles.
What is a gradian (grad)?
A gradian divides a full circle into 400 parts (400 grad = 360°). It was used in surveying and civil engineering, mainly in continental Europe. 100 grad = 90 degrees = a right angle.
What is a "turn" as an angle unit?
1 turn = 360 degrees = 2π radians = 400 gradians. It represents one full rotation. Turns are used in some programming and navigation contexts.
How many radians are in 360 degrees?
360 degrees = 2π radians ≈ 6.28318 radians. One full circle is 2π radians.
When are radians used vs degrees?
Radians are used in mathematics and physics because they simplify formulas (arc length = r × θ). Degrees are used in everyday navigation, maps, and geometry. Most scientific calculators can switch between both.