A 312° 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 48° angle: together they make a full 360° circle.
312° is 13/15 of a full circle, or 26π/15 radians. The minute hand of a clock sweeps 312° in 52 minutes. If you face north and turn 312° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
312° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 48° |
| Radians | 26π/15 ≈ 5.445427 |
| Gradians | 346.6667 grad |
| Fraction of a turn | 13/15 (86.67%) |
| Degrees, minutes, seconds | 312° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 312°
| Function | Value |
|---|---|
| sin 312° | −0.743145 |
| cos 312° | 0.669131 |
| tan 312° | −1.110613 |
312° on a protractor
How to draw a 312° angle with a protractor
- Subtract from 360°: 360° − 312° = 48°. 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 48°.
- Join the vertex to the dot. The inside angle is 48°; the outside angle, going the long way around, is 312°. Draw the angle arc on the outside and label it 312°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 312° directly.
Drawing it a 312° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 9 inches (about 9″) 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 48°, because tan 48° ≈ 1.1106.
- That gives you 48°. The outside (reflex) angle is 312°.
Where you see 312° angles
- The Earth turns 312° on its axis in about 20 h 48 min.
- A 312° 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
312° angle FAQ
What type of angle is 312°?
A 312° angle is a reflex angle, because it is between 180° and 360°.
Does a 312° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 312° is already larger than both. What it does have is an explement (conjugate) of 48°, the angle that completes a full 360° circle.
How many radians is 312 degrees?
312° = 26π/15 radians ≈ 5.4454 rad. To convert degrees to radians, multiply by π/180: 312 × π/180 = 26π/15.
How do I measure a 312° angle on my screen?
Open the online protractor with 312° preset, or type 312 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
