A 327° 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 33° angle: together they make a full 360° circle.
327° is 109/120 of a full circle, or 109π/60 radians. If you face north and turn 327° clockwise, you end up facing between NW and NNW (closest to north-northwest (NNW)).
327° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 33° |
| Radians | 109π/60 ≈ 5.707227 |
| Gradians | 363.3333 grad |
| Fraction of a turn | 109/120 (90.83%) |
| Degrees, minutes, seconds | 327° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to north-northwest (NNW)) |
Trigonometric values of 327°
| Function | Value |
|---|---|
| sin 327° | −0.544639 |
| cos 327° | 0.838671 |
| tan 327° | −0.649408 |
327° on a protractor
How to draw a 327° angle with a protractor
- Subtract from 360°: 360° − 327° = 33°. 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 33°.
- Join the vertex to the dot. The inside angle is 33°; the outside angle, going the long way around, is 327°. Draw the angle arc on the outside and label it 327°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 327° directly.
Drawing it a 327° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 6.49 inches (about 6 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 33°, because tan 33° ≈ 0.6494.
- That gives you 33°. The outside (reflex) angle is 327°.
Where you see 327° angles
- The Earth turns 327° on its axis in about 21 h 48 min.
- A 327° 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
327° angle FAQ
What type of angle is 327°?
A 327° angle is a reflex angle, because it is between 180° and 360°.
Does a 327° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 327° is already larger than both. What it does have is an explement (conjugate) of 33°, the angle that completes a full 360° circle.
How many radians is 327 degrees?
327° = 109π/60 radians ≈ 5.7072 rad. To convert degrees to radians, multiply by π/180: 327 × π/180 = 109π/60.
How do I measure a 327° angle on my screen?
Open the online protractor with 327° preset, or type 327 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
