At 7.5°, this angle is acute, meaning it is narrower than the corner of a square. It is a very narrow angle, just 8.3% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
7.5° is one forty-eighth (1/48) of a full circle, or π/24 radians. If you face north and turn 7.5° clockwise, you end up facing between N and NNE (closest to north (N)).
7.5° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 82.5° |
| Supplement (adds to 180°) | 172.5° |
| Explement (adds to 360°) | 352.5° |
| Radians | π/24 ≈ 0.1309 |
| Gradians | 8.3333 grad |
| Fraction of a turn | one forty-eighth (1/48) (2.08%) |
| Degrees, minutes, seconds | 7° 30′ 0″ |
| Slope (grade) | 13.17% |
| Roof pitch | 1.58/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 7.5°
| Function | Value |
|---|---|
| sin 7.5° | 0.130526 |
| cos 7.5° | 0.991445 |
| tan 7.5° | 0.131652 |
7.5° on a protractor
How to draw a 7.5° 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 7.5° 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. 7.5° falls between the 7° and 8° 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 7.5°.
Drawing it a 7.5° angle without a protractor (compass and ruler)
- Construct a 15° angle, then bisect it.
Where you see 7.5° angles
- Bisecting a 15° angle gives 7.5°, and a 24-sided frame needs 7.5° miters on every piece.
- Divide a circle into 48 equal slices and each slice is 7.5°, e.g. 48 spokes on a wheel or 48 equal pie-chart wedges.
- A board sloped at 7.5° rises about 15.8 inches over a 10-foot (120-inch) run.
- 7.5° of latitude on Earth spans roughly 518 miles north to south.
- The Earth turns 7.5° on its axis in about 30 minutes.
Related angles
7.5° angle FAQ
What type of angle is 7.5°?
A 7.5° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 7.5°?
The complement of 7.5° is 82.5° (together they make 90°), and the supplement is 172.5° (together they make 180°).
How many radians is 7.5 degrees?
7.5° = π/24 radians ≈ 0.1309 rad. To convert degrees to radians, multiply by π/180: 7.5 × π/180 = π/24.
What is 7.5° as a slope or roof pitch?
7.5° is a 13.2% slope, which is a roof pitch of 1.58/12 (a rise of about 1 5/8 inches for every 12 inches of run).
