A 32° angle is classed as acute because it measures less than 90°. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 58°.
32° is 4/45 of a full circle, or 8π/45 radians. If you face north and turn 32° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
32° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 58° |
| Supplement (adds to 180°) | 148° |
| Explement (adds to 360°) | 328° |
| Radians | 8π/45 ≈ 0.558505 |
| Gradians | 35.5556 grad |
| Fraction of a turn | 4/45 (8.89%) |
| Degrees, minutes, seconds | 32° 0′ 0″ |
| Slope (grade) | 62.49% |
| Roof pitch | 7.5/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 32°
| Function | Value |
|---|---|
| sin 32° | 0.529919 |
| cos 32° | 0.848048 |
| tan 32° | 0.624869 |
32° on a protractor
How to draw a 32° 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 32° 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 32°.
Drawing it a 32° 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 6.25 inches (about 6 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 32°, because tan 32° ≈ 0.6249.
Where you see 32° angles
- A board sloped at 32° rises about 75 inches over a 10-foot (120-inch) run.
- 32° of latitude on Earth spans roughly 2,210 miles north to south.
- The Earth turns 32° on its axis in about 2 h 8 min.
- Narrow acute angles like 32° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
32° angle FAQ
What type of angle is 32°?
A 32° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 32°?
The complement of 32° is 58° (together they make 90°), and the supplement is 148° (together they make 180°).
How many radians is 32 degrees?
32° = 8π/45 radians ≈ 0.5585 rad. To convert degrees to radians, multiply by π/180: 32 × π/180 = 8π/45.
What is 32° as a slope or roof pitch?
32° is a 62.5% slope, which is a roof pitch of 7.5/12 (a rise of about 7 1/2 inches for every 12 inches of run).
