At 331°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 29° angle: together they make a full 360° circle.
331° is 331/360 of a full circle, or 331π/180 radians. If you face north and turn 331° clockwise, you end up facing between NW and NNW (closest to north-northwest (NNW)).
331° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 29° |
| Radians | 331π/180 ≈ 5.77704 |
| Gradians | 367.7778 grad |
| Fraction of a turn | 331/360 (91.94%) |
| Degrees, minutes, seconds | 331° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to north-northwest (NNW)) |
Trigonometric values of 331°
| Function | Value |
|---|---|
| sin 331° | −0.48481 |
| cos 331° | 0.87462 |
| tan 331° | −0.554309 |
331° on a protractor
How to draw a 331° angle with a protractor
- Subtract from 360°: 360° − 331° = 29°. 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 29°.
- Join the vertex to the dot. The inside angle is 29°; the outside angle, going the long way around, is 331°. Draw the angle arc on the outside and label it 331°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 331° directly.
Drawing it a 331° 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 5.54 inches (about 5 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 29°, because tan 29° ≈ 0.5543.
- That gives you 29°. The outside (reflex) angle is 331°.
Where you see 331° angles
- The Earth turns 331° on its axis in about 22 h 4 min.
- A 331° 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
331° angle FAQ
What type of angle is 331°?
A 331° angle is a reflex angle, because it is between 180° and 360°.
Does a 331° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 331° is already larger than both. What it does have is an explement (conjugate) of 29°, the angle that completes a full 360° circle.
How many radians is 331 degrees?
331° = 331π/180 radians ≈ 5.777 rad. To convert degrees to radians, multiply by π/180: 331 × π/180 = 331π/180.
How do I measure a 331° angle on my screen?
Open the online protractor with 331° preset, or type 331 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
