A 330° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 30° angle: together they make a full 360° circle.
330° is 11/12 of a full circle, or 11π/6 radians. The minute hand of a clock sweeps 330° in 55 minutes. If you face north and turn 330° clockwise, you end up facing between NW and NNW (closest to north-northwest (NNW)).
330° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 30° |
| Radians | 11π/6 ≈ 5.759587 |
| Gradians | 366.6667 grad |
| Fraction of a turn | 11/12 (91.67%) |
| Degrees, minutes, seconds | 330° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to north-northwest (NNW)) |
Trigonometric values of 330°
| Function | Value |
|---|---|
| sin 330° | −1/2 ≈ −0.5 |
| cos 330° | √3/2 ≈ 0.866025 |
| tan 330° | −√3/3 ≈ −0.57735 |
330° on a protractor
How to draw a 330° angle with a protractor
- Subtract from 360°: 360° − 330° = 30°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 30°.
- Join the vertex to the dot. The inside angle is 30°; the outside angle, going the long way around, is 330°. Draw the angle arc on the outside and label it 330°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 330° directly.
Drawing it a 330° angle without a protractor (compass and ruler)
- Construct a 60° angle, then bisect it.
- That gives you 30°. The reflex angle on the outside of it is 330°.
Where you see 330° angles
- The Earth turns 330° on its axis in about 22 hours.
- A 330° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
330° angle FAQ
What type of angle is 330°?
A 330° angle is a reflex angle, because it is between 180° and 360°.
Does a 330° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 330° is already larger than both. What it does have is an explement (conjugate) of 30°, the angle that completes a full 360° circle.
How many radians is 330 degrees?
330° = 11π/6 radians ≈ 5.7596 rad. To convert degrees to radians, multiply by π/180: 330 × π/180 = 11π/6.
How do I measure a 330° angle on my screen?
Open the online protractor with 330° preset, or type 330 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
