A 9° angle is an acute angle: it is smaller than a right angle (90°). It is a very narrow angle, just 10% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
9° is one fortieth (1/40) of a full circle, or π/20 radians. If you face north and turn 9° clockwise, you end up facing between N and NNE (closest to north (N)).
9° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 81° |
| Supplement (adds to 180°) | 171° |
| Explement (adds to 360°) | 351° |
| Radians | π/20 ≈ 0.15708 |
| Gradians | 10 grad |
| Fraction of a turn | one fortieth (1/40) (2.5%) |
| Degrees, minutes, seconds | 9° 0′ 0″ |
| Slope (grade) | 15.84% |
| Roof pitch | 1.9/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 9°
| Function | Value |
|---|---|
| sin 9° | 0.156434 |
| cos 9° | 0.987688 |
| tan 9° | 0.158384 |
9° on a protractor
How to draw a 9° 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 9° 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 9°.
Drawing it a 9° 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 1.58 inches (about 1 9/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 9°, because tan 9° ≈ 0.1584.
Where you see 9° angles
- A 1:6 dovetail slope, common for softwoods, is about 9.5°.
- Many golf drivers have between 9° and 10.5° of loft.
- Divide a circle into 40 equal slices and each slice is 9°, e.g. 40 spokes on a wheel or 40 equal pie-chart wedges.
- A 20-sided frame (20-sided polygon) is assembled with 9° miter cuts.
- A 2/12 roof pitch is 9.46°, very close to 9°.
- A board sloped at 9° rises about 19 inches over a 10-foot (120-inch) run.
- 9° of latitude on Earth spans roughly 621 miles north to south.
Related angles
9° angle FAQ
What type of angle is 9°?
A 9° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 9°?
The complement of 9° is 81° (together they make 90°), and the supplement is 171° (together they make 180°).
How many radians is 9 degrees?
9° = π/20 radians ≈ 0.1571 rad. To convert degrees to radians, multiply by π/180: 9 × π/180 = π/20.
What is 9° as a slope or roof pitch?
9° is a 15.8% slope, which is a roof pitch of 1.9/12 (a rise of about 1 7/8 inches for every 12 inches of run).
