A 225° 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 135° angle: together they make a full 360° circle.
225° is 5/8 of a full circle, or 5π/4 radians. If you face north and turn 225° clockwise, you end up facing due southwest (SW).
225° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 135° |
| Radians | 5π/4 ≈ 3.926991 |
| Gradians | 250 grad |
| Fraction of a turn | 5/8 (62.5%) |
| Degrees, minutes, seconds | 225° 0′ 0″ |
| Compass bearing | southwest (SW) |
Trigonometric values of 225°
| Function | Value |
|---|---|
| sin 225° | −√2/2 ≈ −0.707107 |
| cos 225° | −√2/2 ≈ −0.707107 |
| tan 225° | 1 |
225° on a protractor
How to draw a 225° angle with a protractor
- Subtract from 360°: 360° − 225° = 135°. 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 135°.
- Join the vertex to the dot. The inside angle is 135°; the outside angle, going the long way around, is 225°. Draw the angle arc on the outside and label it 225°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 225° directly.
Drawing it a 225° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 45° angle: construct a 90° angle, then bisect it.
- What is left between the first arm and the new line is 180° − 45° = 135°.
- That gives you 135°. The reflex angle on the outside of it is 225°.
Where you see 225° angles
- The Earth turns 225° on its axis in about 15 hours.
- A 225° 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
225° angle FAQ
What type of angle is 225°?
A 225° angle is a reflex angle, because it is between 180° and 360°.
Does a 225° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 225° is already larger than both. What it does have is an explement (conjugate) of 135°, the angle that completes a full 360° circle.
How many radians is 225 degrees?
225° = 5π/4 radians ≈ 3.927 rad. To convert degrees to radians, multiply by π/180: 225 × π/180 = 5π/4.
How do I measure a 225° angle on my screen?
Open the online protractor with 225° preset, or type 225 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
