A 270° 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 90° angle: together they make a full 360° circle.
270° is three quarters (3/4) of a full circle, or 3π/2 radians. The minute hand of a clock sweeps 270° in 45 minutes. If you face north and turn 270° clockwise, you end up facing due west (W).
270° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 90° |
| Radians | 3π/2 ≈ 4.712389 |
| Gradians | 300 grad |
| Fraction of a turn | three quarters (3/4) (75%) |
| Degrees, minutes, seconds | 270° 0′ 0″ |
| Compass bearing | west (W) |
Trigonometric values of 270°
| Function | Value |
|---|---|
| sin 270° | −1 |
| cos 270° | 0 |
| tan 270° | undefined |
270° on a protractor
How to draw a 270° angle with a protractor
- Subtract from 360°: 360° − 270° = 90°. 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 90°.
- Join the vertex to the dot. The inside angle is 90°; the outside angle, going the long way around, is 270°. Draw the angle arc on the outside and label it 270°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 270° directly.
Drawing it a 270° angle without a protractor (compass and ruler)
- Construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- That gives you 90°. The reflex angle on the outside of it is 270°.
Where you see 270° angles
- Turning 270° to the right leaves you facing the same way as a 90° left turn.
- West is a compass bearing of 270°.
- The Earth turns 270° on its axis in about 18 hours.
- A 270° 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
270° angle FAQ
What type of angle is 270°?
A 270° angle is a reflex angle, because it is between 180° and 360°.
Does a 270° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 270° is already larger than both. What it does have is an explement (conjugate) of 90°, the angle that completes a full 360° circle.
How many radians is 270 degrees?
270° = 3π/2 radians ≈ 4.7124 rad. To convert degrees to radians, multiply by π/180: 270 × π/180 = 3π/2.
How do I measure a 270° angle on my screen?
Open the online protractor with 270° preset, or type 270 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.