At 271°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of an 89° angle: together they make a full 360° circle.
271° is 271/360 of a full circle, or 271π/180 radians. If you face north and turn 271° clockwise, you end up facing between W and WNW (closest to west (W)).
271° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 89° |
| Radians | 271π/180 ≈ 4.729842 |
| Gradians | 301.1111 grad |
| Fraction of a turn | 271/360 (75.28%) |
| Degrees, minutes, seconds | 271° 0′ 0″ |
| Compass bearing | between W and WNW (closest to west (W)) |
Trigonometric values of 271°
| Function | Value |
|---|---|
| sin 271° | −0.999848 |
| cos 271° | 0.017452 |
| tan 271° | −57.289962 |
271° on a protractor
How to draw a 271° angle with a protractor
- Subtract from 360°: 360° − 271° = 89°. 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 89°.
- Join the vertex to the dot. The inside angle is 89°; the outside angle, going the long way around, is 271°. Draw the angle arc on the outside and label it 271°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 271° directly.
Drawing it a 271° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 0.17 inches (about 3/16″) 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 89°, because tan 89° ≈ 57.29.
- That gives you 89°. The outside (reflex) angle is 271°.
Where you see 271° angles
- The Earth turns 271° on its axis in about 18 h 4 min.
- A 271° 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
271° angle FAQ
What type of angle is 271°?
A 271° angle is a reflex angle, because it is between 180° and 360°.
Does a 271° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 271° is already larger than both. What it does have is an explement (conjugate) of 89°, the angle that completes a full 360° circle.
How many radians is 271 degrees?
271° = 271π/180 radians ≈ 4.7298 rad. To convert degrees to radians, multiply by π/180: 271 × π/180 = 271π/180.
How do I measure a 271° angle on my screen?
Open the online protractor with 271° preset, or type 271 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
