At 181°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 179° angle: together they make a full 360° circle.
181° is 181/360 of a full circle, or 181π/180 radians. If you face north and turn 181° clockwise, you end up facing between S and SSW (closest to south (S)).
181° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 179° |
| Radians | 181π/180 ≈ 3.159046 |
| Gradians | 201.1111 grad |
| Fraction of a turn | 181/360 (50.28%) |
| Degrees, minutes, seconds | 181° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south (S)) |
Trigonometric values of 181°
| Function | Value |
|---|---|
| sin 181° | −0.017452 |
| cos 181° | −0.999848 |
| tan 181° | 0.017455 |
181° on a protractor
How to draw a 181° angle with a protractor
- Subtract from 360°: 360° − 181° = 179°. 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 179°.
- Join the vertex to the dot. The inside angle is 179°; the outside angle, going the long way around, is 181°. Draw the angle arc on the outside and label it 181°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 181° directly.
Drawing it a 181° angle without a protractor (rise and run method)
- 181° = 180° − 1°. Draw a straight line, pick a vertex on it, and build a 1° angle on one side as follows; the angle on the other side of the new line is 179°.
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 0.17 inches (about 3/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 1°, because tan 1° ≈ 0.0175.
- That gives you 179°. The outside (reflex) angle is 181°.
Where you see 181° angles
- The Earth turns 181° on its axis in about 12 h 4 min.
- A 181° 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
181° angle FAQ
What type of angle is 181°?
A 181° angle is a reflex angle, because it is between 180° and 360°.
Does a 181° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 181° is already larger than both. What it does have is an explement (conjugate) of 179°, the angle that completes a full 360° circle.
How many radians is 181 degrees?
181° = 181π/180 radians ≈ 3.159 rad. To convert degrees to radians, multiply by π/180: 181 × π/180 = 181π/180.
How do I measure a 181° angle on my screen?
Open the online protractor with 181° preset, or type 181 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
