A 261° 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 99° angle: together they make a full 360° circle.
261° is 29/40 of a full circle, or 29π/20 radians. If you face north and turn 261° clockwise, you end up facing between WSW and W (closest to west (W)).
261° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 99° |
| Radians | 29π/20 ≈ 4.555309 |
| Gradians | 290 grad |
| Fraction of a turn | 29/40 (72.5%) |
| Degrees, minutes, seconds | 261° 0′ 0″ |
| Compass bearing | between WSW and W (closest to west (W)) |
Trigonometric values of 261°
| Function | Value |
|---|---|
| sin 261° | −0.987688 |
| cos 261° | −0.156434 |
| tan 261° | 6.313752 |
261° on a protractor
How to draw a 261° angle with a protractor
- Subtract from 360°: 360° − 261° = 99°. 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 99°.
- Join the vertex to the dot. The inside angle is 99°; the outside angle, going the long way around, is 261°. Draw the angle arc on the outside and label it 261°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 261° directly.
Drawing it a 261° angle without a protractor (rise and run method)
- 261° = 180° − 81°. Draw a straight line, pick a vertex on it, and build an 81° angle on one side as follows; the angle on the other side of the new line is 99°.
- Draw a straight baseline and measure 1.58 inches (about 1 9/16″) 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 81°, because tan 81° ≈ 6.3138.
- That gives you 99°. The outside (reflex) angle is 261°.
Where you see 261° angles
- The Earth turns 261° on its axis in about 17 h 24 min.
- A 261° 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
261° angle FAQ
What type of angle is 261°?
A 261° angle is a reflex angle, because it is between 180° and 360°.
Does a 261° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 261° is already larger than both. What it does have is an explement (conjugate) of 99°, the angle that completes a full 360° circle.
How many radians is 261 degrees?
261° = 29π/20 radians ≈ 4.5553 rad. To convert degrees to radians, multiply by π/180: 261 × π/180 = 29π/20.
How do I measure a 261° angle on my screen?
Open the online protractor with 261° preset, or type 261 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
