A 315° 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 45° angle: together they make a full 360° circle.
315° is 7/8 of a full circle, or 7π/4 radians. If you face north and turn 315° clockwise, you end up facing due northwest (NW).
315° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 45° |
| Radians | 7π/4 ≈ 5.497787 |
| Gradians | 350 grad |
| Fraction of a turn | 7/8 (87.5%) |
| Degrees, minutes, seconds | 315° 0′ 0″ |
| Compass bearing | northwest (NW) |
Trigonometric values of 315°
| Function | Value |
|---|---|
| sin 315° | −√2/2 ≈ −0.707107 |
| cos 315° | √2/2 ≈ 0.707107 |
| tan 315° | −1 |
315° on a protractor
How to draw a 315° angle with a protractor
- Subtract from 360°: 360° − 315° = 45°. 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 45°.
- Join the vertex to the dot. The inside angle is 45°; the outside angle, going the long way around, is 315°. Draw the angle arc on the outside and label it 315°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 315° directly.
Drawing it a 315° angle without a protractor (compass and ruler)
- Construct a 90° angle, then bisect it.
- That gives you 45°. The reflex angle on the outside of it is 315°.
Where you see 315° angles
- The Earth turns 315° on its axis in about 21 hours.
- A 315° 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
315° angle FAQ
What type of angle is 315°?
A 315° angle is a reflex angle, because it is between 180° and 360°.
Does a 315° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 315° is already larger than both. What it does have is an explement (conjugate) of 45°, the angle that completes a full 360° circle.
How many radians is 315 degrees?
315° = 7π/4 radians ≈ 5.4978 rad. To convert degrees to radians, multiply by π/180: 315 × π/180 = 7π/4.
How do I measure a 315° angle on my screen?
Open the online protractor with 315° preset, or type 315 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
