At 22°, 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 68°.
22° is 11/180 of a full circle, or 11π/90 radians. If you face north and turn 22° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
22° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 68° |
| Supplement (adds to 180°) | 158° |
| Explement (adds to 360°) | 338° |
| Radians | 11π/90 ≈ 0.383972 |
| Gradians | 24.4444 grad |
| Fraction of a turn | 11/180 (6.11%) |
| Degrees, minutes, seconds | 22° 0′ 0″ |
| Slope (grade) | 40.4% |
| Roof pitch | 4.85/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 22°
| Function | Value |
|---|---|
| sin 22° | 0.374607 |
| cos 22° | 0.927184 |
| tan 22° | 0.404026 |
22° on a protractor
How to draw a 22° 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 22° 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 22°.
Drawing it a 22° 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 4.04 inches (about 4 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 22°, because tan 22° ≈ 0.404.
Where you see 22° angles
- A board sloped at 22° rises about 48.5 inches over a 10-foot (120-inch) run.
- 22° of latitude on Earth spans roughly 1,519 miles north to south.
- The Earth turns 22° on its axis in about 1 h 28 min.
- Narrow acute angles like 22° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
22° angle FAQ
What type of angle is 22°?
A 22° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 22°?
The complement of 22° is 68° (together they make 90°), and the supplement is 158° (together they make 180°).
How many radians is 22 degrees?
22° = 11π/90 radians ≈ 0.384 rad. To convert degrees to radians, multiply by π/180: 22 × π/180 = 11π/90.
What is 22° as a slope or roof pitch?
22° is a 40.4% slope, which is a roof pitch of 4.85/12 (a rise of about 4 7/8 inches for every 12 inches of run).
