A 186° 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 174° angle: together they make a full 360° circle.
186° is 31/60 of a full circle, or 31π/30 radians. The minute hand of a clock sweeps 186° in 31 minutes. If you face north and turn 186° clockwise, you end up facing between S and SSW (closest to south (S)).
186° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 174° |
| Radians | 31π/30 ≈ 3.246312 |
| Gradians | 206.6667 grad |
| Fraction of a turn | 31/60 (51.67%) |
| Degrees, minutes, seconds | 186° 0′ 0″ |
| Compass bearing | between S and SSW (closest to south (S)) |
Trigonometric values of 186°
| Function | Value |
|---|---|
| sin 186° | −0.104528 |
| cos 186° | −0.994522 |
| tan 186° | 0.105104 |
186° on a protractor
How to draw a 186° angle with a protractor
- Subtract from 360°: 360° − 186° = 174°. 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 174°.
- Join the vertex to the dot. The inside angle is 174°; the outside angle, going the long way around, is 186°. Draw the angle arc on the outside and label it 186°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 186° directly.
Drawing it a 186° angle without a protractor (rise and run method)
- 186° = 180° − 6°. Draw a straight line, pick a vertex on it, and build a 6° angle on one side as follows; the angle on the other side of the new line is 174°.
- 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 1.05 inches (about 1 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 6°, because tan 6° ≈ 0.1051.
- That gives you 174°. The outside (reflex) angle is 186°.
Where you see 186° angles
- The Earth turns 186° on its axis in about 12 h 24 min.
- A 186° 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
186° angle FAQ
What type of angle is 186°?
A 186° angle is a reflex angle, because it is between 180° and 360°.
Does a 186° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 186° is already larger than both. What it does have is an explement (conjugate) of 174°, the angle that completes a full 360° circle.
How many radians is 186 degrees?
186° = 31π/30 radians ≈ 3.2463 rad. To convert degrees to radians, multiply by π/180: 186 × π/180 = 31π/30.
How do I measure a 186° angle on my screen?
Open the online protractor with 186° preset, or type 186 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
