At 31°, this angle is acute, meaning it is narrower than the corner of a square. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 59°.
31° is 31/360 of a full circle, or 31π/180 radians. If you face north and turn 31° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
31° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 59° |
| Supplement (adds to 180°) | 149° |
| Explement (adds to 360°) | 329° |
| Radians | 31π/180 ≈ 0.541052 |
| Gradians | 34.4444 grad |
| Fraction of a turn | 31/360 (8.61%) |
| Degrees, minutes, seconds | 31° 0′ 0″ |
| Slope (grade) | 60.09% |
| Roof pitch | 7.21/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 31°
| Function | Value |
|---|---|
| sin 31° | 0.515038 |
| cos 31° | 0.857167 |
| tan 31° | 0.600861 |
31° on a protractor
How to draw a 31° 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 31° 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 31°.
Drawing it a 31° angle without a protractor (rise and run method)
- 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 6.01 inches (about 6″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 31°, because tan 31° ≈ 0.6009.
Where you see 31° angles
- A board sloped at 31° rises about 72.1 inches over a 10-foot (120-inch) run.
- 31° of latitude on Earth spans roughly 2,141 miles north to south.
- The Earth turns 31° on its axis in about 2 h 4 min.
- Narrow acute angles like 31° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
31° angle FAQ
What type of angle is 31°?
A 31° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 31°?
The complement of 31° is 59° (together they make 90°), and the supplement is 149° (together they make 180°).
How many radians is 31 degrees?
31° = 31π/180 radians ≈ 0.5411 rad. To convert degrees to radians, multiply by π/180: 31 × π/180 = 31π/180.
What is 31° as a slope or roof pitch?
31° is a 60.1% slope, which is a roof pitch of 7.21/12 (a rise of about 7 1/4 inches for every 12 inches of run).
