A 314° angle is reflex because it measures between 180° and 360°. It is the "outside" of a 46° angle: together they make a full 360° circle.
314° is 157/180 of a full circle, or 157π/90 radians. If you face north and turn 314° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
314° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 46° |
| Radians | 157π/90 ≈ 5.480334 |
| Gradians | 348.8889 grad |
| Fraction of a turn | 157/180 (87.22%) |
| Degrees, minutes, seconds | 314° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 314°
| Function | Value |
|---|---|
| sin 314° | −0.71934 |
| cos 314° | 0.694658 |
| tan 314° | −1.03553 |
314° on a protractor
How to draw a 314° angle with a protractor
- Subtract from 360°: 360° − 314° = 46°. 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 46°.
- Join the vertex to the dot. The inside angle is 46°; the outside angle, going the long way around, is 314°. Draw the angle arc on the outside and label it 314°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 314° directly.
Drawing it a 314° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 9.66 inches (about 9 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 46°, because tan 46° ≈ 1.0355.
- That gives you 46°. The outside (reflex) angle is 314°.
Where you see 314° angles
- The Earth turns 314° on its axis in about 20 h 56 min.
- A 314° 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
314° angle FAQ
What type of angle is 314°?
A 314° angle is a reflex angle, because it is between 180° and 360°.
Does a 314° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 314° is already larger than both. What it does have is an explement (conjugate) of 46°, the angle that completes a full 360° circle.
How many radians is 314 degrees?
314° = 157π/90 radians ≈ 5.4803 rad. To convert degrees to radians, multiply by π/180: 314 × π/180 = 157π/90.
How do I measure a 314° angle on my screen?
Open the online protractor with 314° preset, or type 314 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
