A 321° 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 39° angle: together they make a full 360° circle.
321° is 107/120 of a full circle, or 107π/60 radians. If you face north and turn 321° clockwise, you end up facing between NW and NNW (closest to northwest (NW)).
321° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 39° |
| Radians | 107π/60 ≈ 5.602507 |
| Gradians | 356.6667 grad |
| Fraction of a turn | 107/120 (89.17%) |
| Degrees, minutes, seconds | 321° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to northwest (NW)) |
Trigonometric values of 321°
| Function | Value |
|---|---|
| sin 321° | −0.62932 |
| cos 321° | 0.777146 |
| tan 321° | −0.809784 |
321° on a protractor
How to draw a 321° angle with a protractor
- Subtract from 360°: 360° − 321° = 39°. 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 39°.
- Join the vertex to the dot. The inside angle is 39°; the outside angle, going the long way around, is 321°. Draw the angle arc on the outside and label it 321°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 321° directly.
Drawing it a 321° 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 8.1 inches (about 8 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 39°, because tan 39° ≈ 0.8098.
- That gives you 39°. The outside (reflex) angle is 321°.
Where you see 321° angles
- The Earth turns 321° on its axis in about 21 h 24 min.
- A 321° 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
321° angle FAQ
What type of angle is 321°?
A 321° angle is a reflex angle, because it is between 180° and 360°.
Does a 321° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 321° is already larger than both. What it does have is an explement (conjugate) of 39°, the angle that completes a full 360° circle.
How many radians is 321 degrees?
321° = 107π/60 radians ≈ 5.6025 rad. To convert degrees to radians, multiply by π/180: 321 × π/180 = 107π/60.
How do I measure a 321° angle on my screen?
Open the online protractor with 321° preset, or type 321 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
