A 6° angle is an acute angle: it is smaller than a right angle (90°). It is a very narrow angle, just 6.7% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
6° is one sixtieth (1/60) of a full circle, or π/30 radians. The minute hand of a clock sweeps 6° in 1 minute. If you face north and turn 6° clockwise, you end up facing between N and NNE (closest to north (N)).
6° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 84° |
| Supplement (adds to 180°) | 174° |
| Explement (adds to 360°) | 354° |
| Radians | π/30 ≈ 0.10472 |
| Gradians | 6.6667 grad |
| Fraction of a turn | one sixtieth (1/60) (1.67%) |
| Degrees, minutes, seconds | 6° 0′ 0″ |
| Slope (grade) | 10.51% |
| Roof pitch | 1.26/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 6°
| Function | Value |
|---|---|
| sin 6° | 0.104528 |
| cos 6° | 0.994522 |
| tan 6° | 0.105104 |
6° on a protractor
How to draw a 6° 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 6° 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 6°.
Drawing it a 6° 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 1.05 inches (about 1 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 6°, because tan 6° ≈ 0.1051.
Where you see 6° angles
- The minute hand of a clock moves exactly 6° every minute (360° ÷ 60).
- Divide a circle into 60 equal slices and each slice is 6°, e.g. 60 spokes on a wheel or 60 equal pie-chart wedges.
- A 30-sided frame (30-sided polygon) is assembled with 6° miter cuts.
- A board sloped at 6° rises about 12.6 inches over a 10-foot (120-inch) run.
- 6° of latitude on Earth spans roughly 414 miles north to south.
- The Earth turns 6° on its axis in about 24 minutes.
Related angles
6° angle FAQ
What type of angle is 6°?
A 6° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 6°?
The complement of 6° is 84° (together they make 90°), and the supplement is 174° (together they make 180°).
How many radians is 6 degrees?
6° = π/30 radians ≈ 0.1047 rad. To convert degrees to radians, multiply by π/180: 6 × π/180 = π/30.
What is 6° as a slope or roof pitch?
6° is a 10.5% slope, which is a roof pitch of 1.26/12 (a rise of about 1 1/4 inches for every 12 inches of run).
