At 67.5°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 22.5° more and you get a square corner.
67.5° is 3/16 of a full circle, or 3π/8 radians. If you face north and turn 67.5° clockwise, you end up facing due east-northeast (ENE).
67.5° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 22.5° |
| Supplement (adds to 180°) | 112.5° |
| Explement (adds to 360°) | 292.5° |
| Radians | 3π/8 ≈ 1.178097 |
| Gradians | 75 grad |
| Fraction of a turn | 3/16 (18.75%) |
| Degrees, minutes, seconds | 67° 30′ 0″ |
| Slope (grade) | 241.42% |
| Roof pitch | 28.97/12 |
| Compass bearing | east-northeast (ENE) |
Trigonometric values of 67.5°
| Function | Value |
|---|---|
| sin 67.5° | √(2 + √2)/2 ≈ 0.92388 |
| cos 67.5° | √(2 − √2)/2 ≈ 0.382683 |
| tan 67.5° | √2 + 1 ≈ 2.414214 |
67.5° on a protractor
How to draw a 67.5° 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 67.5° 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. 67.5° falls between the 67° and 68° 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 67.5°.
Drawing it a 67.5° angle without a protractor (compass and ruler)
- Draw a 90° angle: construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- Inside it, starting from the second arm, mark a 22.5° angle: construct a 45° angle, then bisect it.
- What is left between the first arm and the new line is 90° − 22.5° = 67.5°.
Where you see 67.5° angles
- 67.5° of latitude on Earth spans roughly 4,661 miles north to south.
- The Earth turns 67.5° on its axis in about 4 h 30 min.
- Narrow acute angles like 67.5° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
67.5° angle FAQ
What type of angle is 67.5°?
A 67.5° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 67.5°?
The complement of 67.5° is 22.5° (together they make 90°), and the supplement is 112.5° (together they make 180°).
How many radians is 67.5 degrees?
67.5° = 3π/8 radians ≈ 1.1781 rad. To convert degrees to radians, multiply by π/180: 67.5 × π/180 = 3π/8.
What is 67.5° as a slope or roof pitch?
67.5° is a 241.4% slope, which is a roof pitch of 28.97/12 (a rise of about 29 inches for every 12 inches of run).
