A 360° angle is a full angle (a complete turn): the rotating arm travels all the way around and lands back on the starting arm. It is equal to four right angles or two straight angles, and it is the total of all angles around a point.
360° is one full turn of a full circle, or 2π radians. The minute hand of a clock sweeps 360° in 60 minutes. If you face north and turn 360° clockwise, you end up facing due north (N).
360° angle facts
| Angle type | Full angle (exactly 360°) |
|---|---|
| Radians | 2π ≈ 6.283185 |
| Gradians | 400 grad |
| Fraction of a turn | one full turn (100%) |
| Degrees, minutes, seconds | 360° 0′ 0″ |
| Compass bearing | north (N) |
Trigonometric values of 360°
| Function | Value |
|---|---|
| sin 360° | 0 |
| cos 360° | 1 |
| tan 360° | 0 |
360° on a protractor
How to draw a 360° angle with a protractor
- Draw a ray (a line from a starting point).
- Imagine rotating it all the way around the starting point until it lands back on itself: that rotation is 360°.
- Show it with a full circle arc (and an arrow) around the vertex, labeled 360°.
Where you see 360° angles
- A full rotation, like a wheel making one complete turn, is 360°.
- In skateboarding and snowboarding, a "360" is one full spin.
- A 360° camera captures the view in every direction around it.
- The Earth turns 360° on its axis in about 24 hours.
Related angles
360° angle FAQ
What type of angle is 360°?
A 360° angle is a full angle, because it is exactly 360°.
How many radians is 360 degrees?
360° = 2π radians ≈ 6.2832 rad. To convert degrees to radians, multiply by π/180: 360 × π/180 = 2π.