Angle Converter
An angle converter converts between degrees, radians, gradians, and turns. Degrees (0–360) are used in everyday life. Radians (0–2π) are the mathematical standard. Gradians divide a right angle into 100 units.
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Tip: Mental conversion: 1 radian ≈ 57.3°. So π/4 rad = 45° (half of 90°), π/3 rad = 60°.
- 1360° = 2π radians = 400 gradians = 1 turn
- 2Degrees to radians: multiply by π/180
- 3Radians to degrees: multiply by 180/π
- 41 gradian = 0.9 degrees = π/200 radians
| Degrees | Radians | Gradians | Description |
|---|---|---|---|
| 0° | 0 | 0 | Zero angle |
| 30° | π/6 ≈ 0.5236 | 33.33 | Interior angle of equilateral triangle |
| 45° | π/4 ≈ 0.7854 | 50 | Diagonal angle |
| 90° | π/2 ≈ 1.5708 | 100 | Right angle |
| 180° | π ≈ 3.1416 | 200 | Straight line |
| 360° | 2π ≈ 6.2832 | 400 | Full rotation |
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Fun Fact
Radians were introduced to mathematics in the 1700s and are preferred in calculus because they make derivatives of sin and cos much simpler — no conversion factors needed.
References
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