A 311° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 49° angle: together they make a full 360° circle.
311° is 311/360 of a full circle, or 311π/180 radians. If you face north and turn 311° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
311° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 49° |
| Radians | 311π/180 ≈ 5.427974 |
| Gradians | 345.5556 grad |
| Fraction of a turn | 311/360 (86.39%) |
| Degrees, minutes, seconds | 311° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 311°
| Function | Value |
|---|---|
| sin 311° | −0.75471 |
| cos 311° | 0.656059 |
| tan 311° | −1.150368 |
311° on a protractor
How to draw a 311° angle with a protractor
- Subtract from 360°: 360° − 311° = 49°. 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 49°.
- Join the vertex to the dot. The inside angle is 49°; the outside angle, going the long way around, is 311°. Draw the angle arc on the outside and label it 311°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 311° directly.
Drawing it a 311° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 8.69 inches (about 8 11/16″) 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 49°, because tan 49° ≈ 1.1504.
- That gives you 49°. The outside (reflex) angle is 311°.
Where you see 311° angles
- The Earth turns 311° on its axis in about 20 h 44 min.
- A 311° 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
311° angle FAQ
What type of angle is 311°?
A 311° angle is a reflex angle, because it is between 180° and 360°.
Does a 311° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 311° is already larger than both. What it does have is an explement (conjugate) of 49°, the angle that completes a full 360° circle.
How many radians is 311 degrees?
311° = 311π/180 radians ≈ 5.428 rad. To convert degrees to radians, multiply by π/180: 311 × π/180 = 311π/180.
How do I measure a 311° angle on my screen?
Open the online protractor with 311° preset, or type 311 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
