📐 Trigonometry & Geometry
Angle & Degree Unit Converter
Convert plane angles between Degrees, Radians, Gradians, Arcminutes, Arcseconds, and Revolutions.
Key Angles:
180° = π Radians
90° Right Angle = 100 Gradians
1 Radian in Degrees
360° Full Circle (1 Rev)
Conversion Result
3.141593 Radians
Live Multi-Angle Comparison:
Degrees
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Radians
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Gradians
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Revolutions
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Geometric & Trigonometric Angle Standards
An angle represents the rotational measure between two intersecting line rays. While degrees trace back to ancient Babylonian base-60 astronomy, radians are the natural mathematical unit of angle measurement because arc length $s = r \theta$.
Trigonometric Unit Circle Angle Equivalents
| Fraction of Circle | Degrees (°) | Radians (rad) | Gradians (grad) |
|---|---|---|---|
| $1/12$ Circle | 30° | $\pi / 6 \approx 0.5236$ | 33.33 grad |
| $1/8$ Circle | 45° | $\pi / 4 \approx 0.7854$ | 50 grad |
| $1/6$ Circle | 60° | $\pi / 3 \approx 1.0472$ | 66.67 grad |
| $1/4$ Circle (Right Angle) | 90° | $\pi / 2 \approx 1.5708$ | 100 grad |
| $1/2$ Circle (Straight) | 180° | $\pi \approx 3.14159$ | 200 grad |
| Full Circle | 360° | $2\pi \approx 6.28318$ | 400 grad |