๐ Degree (ยฐ) โ Radian (rad) Converter
Convert between degrees and radians.
Conversion Formula
Radian = Degree ร (ฯ / 180)
Degree = Radian ร (180 / ฯ)
One radian is the central angle subtended by an arc equal in length to the radius. Therefore, the circumference 2ฯr of a circle with radius r equals 2ฯ radians.
Key Angle Conversion Table
| Degree (ยฐ) | Radian (rad) | ฯ Expression |
|---|---|---|
| 0ยฐ | 0 | 0 |
| 30ยฐ | 0.5236 | ฯ/6 |
| 45ยฐ | 0.7854 | ฯ/4 |
| 60ยฐ | 1.0472 | ฯ/3 |
| 90ยฐ | 1.5708 | ฯ/2 |
| 120ยฐ | 2.0944 | 2ฯ/3 |
| 180ยฐ | 3.1416 | ฯ |
| 270ยฐ | 4.7124 | 3ฯ/2 |
| 360ยฐ | 6.2832 | 2ฯ |
Unit Circle and Trigonometry
The point (cos ฮธ, sin ฮธ) on the unit circle (radius=1) visually represents angle ฮธ. The red dot in the left diagram is this point.
x = cos ฮธ, y = sin ฮธ