At 313°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 47° angle: together they make a full 360° circle.
313° is 313/360 of a full circle, or 313π/180 radians. If you face north and turn 313° clockwise, you end up facing between WNW and NW (closest to northwest (NW)).
313° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 47° |
| Radians | 313π/180 ≈ 5.462881 |
| Gradians | 347.7778 grad |
| Fraction of a turn | 313/360 (86.94%) |
| Degrees, minutes, seconds | 313° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to northwest (NW)) |
Trigonometric values of 313°
| Function | Value |
|---|---|
| sin 313° | −0.731354 |
| cos 313° | 0.681998 |
| tan 313° | −1.072369 |
313° on a protractor
How to draw a 313° angle with a protractor
- Subtract from 360°: 360° − 313° = 47°. 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 47°.
- Join the vertex to the dot. The inside angle is 47°; the outside angle, going the long way around, is 313°. Draw the angle arc on the outside and label it 313°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 313° directly.
Drawing it a 313° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 9.33 inches (about 9 5/16″) 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 47°, because tan 47° ≈ 1.0724.
- That gives you 47°. The outside (reflex) angle is 313°.
Where you see 313° angles
- The Earth turns 313° on its axis in about 20 h 52 min.
- A 313° 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
313° angle FAQ
What type of angle is 313°?
A 313° angle is a reflex angle, because it is between 180° and 360°.
Does a 313° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 313° is already larger than both. What it does have is an explement (conjugate) of 47°, the angle that completes a full 360° circle.
How many radians is 313 degrees?
313° = 313π/180 radians ≈ 5.4629 rad. To convert degrees to radians, multiply by π/180: 313 × π/180 = 313π/180.
How do I measure a 313° angle on my screen?
Open the online protractor with 313° preset, or type 313 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
