At 22.5°, 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 67.5°.
22.5° is one sixteenth (1/16) of a full circle, or π/8 radians. If you face north and turn 22.5° clockwise, you end up facing due north-northeast (NNE).
22.5° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 67.5° |
| Supplement (adds to 180°) | 157.5° |
| Explement (adds to 360°) | 337.5° |
| Radians | π/8 ≈ 0.392699 |
| Gradians | 25 grad |
| Fraction of a turn | one sixteenth (1/16) (6.25%) |
| Degrees, minutes, seconds | 22° 30′ 0″ |
| Slope (grade) | 41.42% |
| Roof pitch | 4.97/12 |
| Compass bearing | north-northeast (NNE) |
Trigonometric values of 22.5°
| Function | Value |
|---|---|
| sin 22.5° | √(2 − √2)/2 ≈ 0.382683 |
| cos 22.5° | √(2 + √2)/2 ≈ 0.92388 |
| tan 22.5° | √2 − 1 ≈ 0.414214 |
22.5° on a protractor
How to draw a 22.5° 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 22.5° 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. 22.5° falls between the 22° and 23° marks; estimate the position carefully.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with an arc and label it 22.5°.
Drawing it a 22.5° angle without a protractor (compass and ruler)
- Construct a 45° angle, then bisect it.
- Paper method: fold a square corner to corner (45°), then fold the edge onto the diagonal to halve it again.
Where you see 22.5° angles
- North-northeast (NNE) on a compass is a bearing of 22.5°.
- An eight-sided frame, the shape of a stop sign, is joined with 22.5° miters.
- Divide a circle into 16 equal slices and each slice is 22.5°, e.g. 16 spokes on a wheel or 16 equal pie-chart wedges.
- A 5/12 roof pitch is 22.62°, very close to 22.5°.
- A board sloped at 22.5° rises about 49.7 inches over a 10-foot (120-inch) run.
- 22.5° of latitude on Earth spans roughly 1,554 miles north to south.
- The Earth turns 22.5° on its axis in about 1 h 30 min.
Related angles
22.5° angle FAQ
What type of angle is 22.5°?
A 22.5° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 22.5°?
The complement of 22.5° is 67.5° (together they make 90°), and the supplement is 157.5° (together they make 180°).
How many radians is 22.5 degrees?
22.5° = π/8 radians ≈ 0.3927 rad. To convert degrees to radians, multiply by π/180: 22.5 × π/180 = π/8.
What is 22.5° as a slope or roof pitch?
22.5° is a 41.4% slope, which is a roof pitch of 4.97/12 (a rise of about 5 inches for every 12 inches of run).