An 81° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 9° more and you get a square corner.
81° is 9/40 of a full circle, or 9π/20 radians. If you face north and turn 81° clockwise, you end up facing between ENE and E (closest to east (E)).
81° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 9° |
| Supplement (adds to 180°) | 99° |
| Explement (adds to 360°) | 279° |
| Radians | 9π/20 ≈ 1.413717 |
| Gradians | 90 grad |
| Fraction of a turn | 9/40 (22.5%) |
| Degrees, minutes, seconds | 81° 0′ 0″ |
| Slope (grade) | 631.38% |
| Roof pitch | 75.77/12 |
| Compass bearing | between ENE and E (closest to east (E)) |
Trigonometric values of 81°
| Function | Value |
|---|---|
| sin 81° | 0.987688 |
| cos 81° | 0.156434 |
| tan 81° | 6.313752 |
81° on a protractor
How to draw an 81° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 81° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 81°.
Drawing it an 81° angle without a protractor (rise and run method)
- 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.
Where you see 81° angles
- 81° of latitude on Earth spans roughly 5,593 miles north to south.
- The Earth turns 81° on its axis in about 5 h 24 min.
- Narrow acute angles like 81° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
81° angle FAQ
What type of angle is 81°?
An 81° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 81°?
The complement of 81° is 9° (together they make 90°), and the supplement is 99° (together they make 180°).
How many radians is 81 degrees?
81° = 9π/20 radians ≈ 1.4137 rad. To convert degrees to radians, multiply by π/180: 81 × π/180 = 9π/20.
How do I measure an 81° angle on my screen?
Open the online protractor with 81° preset, or type 81 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
