At 322°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 38° angle: together they make a full 360° circle.
322° is 161/180 of a full circle, or 161π/90 radians. If you face north and turn 322° clockwise, you end up facing between NW and NNW (closest to northwest (NW)).
322° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 38° |
| Radians | 161π/90 ≈ 5.61996 |
| Gradians | 357.7778 grad |
| Fraction of a turn | 161/180 (89.44%) |
| Degrees, minutes, seconds | 322° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to northwest (NW)) |
Trigonometric values of 322°
| Function | Value |
|---|---|
| sin 322° | −0.615661 |
| cos 322° | 0.788011 |
| tan 322° | −0.781286 |
322° on a protractor
How to draw a 322° angle with a protractor
- Subtract from 360°: 360° − 322° = 38°. 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 38°.
- Join the vertex to the dot. The inside angle is 38°; the outside angle, going the long way around, is 322°. Draw the angle arc on the outside and label it 322°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 322° directly.
Drawing it a 322° 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 7.81 inches (about 7 13/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 38°, because tan 38° ≈ 0.7813.
- That gives you 38°. The outside (reflex) angle is 322°.
Where you see 322° angles
- The Earth turns 322° on its axis in about 21 h 28 min.
- A 322° 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
322° angle FAQ
What type of angle is 322°?
A 322° angle is a reflex angle, because it is between 180° and 360°.
Does a 322° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 322° is already larger than both. What it does have is an explement (conjugate) of 38°, the angle that completes a full 360° circle.
How many radians is 322 degrees?
322° = 161π/90 radians ≈ 5.62 rad. To convert degrees to radians, multiply by π/180: 322 × π/180 = 161π/90.
How do I measure a 322° angle on my screen?
Open the online protractor with 322° preset, or type 322 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
