A 306° 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 54° angle: together they make a full 360° circle.
306° is 17/20 of a full circle, or 17π/10 radians. The minute hand of a clock sweeps 306° in 51 minutes. If you face north and turn 306° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
306° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 54° |
| Radians | 17π/10 ≈ 5.340708 |
| Gradians | 340 grad |
| Fraction of a turn | 17/20 (85%) |
| Degrees, minutes, seconds | 306° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 306°
| Function | Value |
|---|---|
| sin 306° | −(√5 + 1)/4 ≈ −0.809017 |
| cos 306° | √(10 − 2√5)/4 ≈ 0.587785 |
| tan 306° | −1.376382 |
306° on a protractor
How to draw a 306° angle with a protractor
- Subtract from 360°: 360° − 306° = 54°. 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 54°.
- Join the vertex to the dot. The inside angle is 54°; the outside angle, going the long way around, is 306°. Draw the angle arc on the outside and label it 306°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 306° directly.
Drawing it a 306° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7.27 inches (about 7 1/4″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 54°, because tan 54° ≈ 1.3764.
- That gives you 54°. The outside (reflex) angle is 306°.
Where you see 306° angles
- The Earth turns 306° on its axis in about 20 h 24 min.
- A 306° 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
306° angle FAQ
What type of angle is 306°?
A 306° angle is a reflex angle, because it is between 180° and 360°.
Does a 306° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 306° is already larger than both. What it does have is an explement (conjugate) of 54°, the angle that completes a full 360° circle.
How many radians is 306 degrees?
306° = 17π/10 radians ≈ 5.3407 rad. To convert degrees to radians, multiply by π/180: 306 × π/180 = 17π/10.
How do I measure a 306° angle on my screen?
Open the online protractor with 306° preset, or type 306 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
