360 Degree Angle

Full angle · 2π ≈ 6.283185 radians · one full turn (100%) of a circle

Diagram of a 360 degree angle360°
Full angle: 360°
Angle type
Full angle
Radians
2π ≈ 6.283185
Open 360° in the online protractor

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°

FunctionValue
sin 360° 0
cos 360° 1
tan 360° 0

360° on a protractor

Protractor showing 360 degrees0102030405060708090100110120130140150160170180190200210220230240250260270280290300310320330340350360°
On a 360° protractor, read 360° directly going counter-clockwise from 0°. Try it in the interactive protractor →

How to draw a 360° angle with a protractor

  1. Draw a ray (a line from a starting point).
  2. Imagine rotating it all the way around the starting point until it lands back on itself: that rotation is 360°.
  3. 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.

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.