A 12° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 78°.
12° is one thirtieth (1/30) of a full circle, or π/15 radians. The minute hand of a clock sweeps 12° in 2 minutes. If you face north and turn 12° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
12° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 78° |
| Supplement (adds to 180°) | 168° |
| Explement (adds to 360°) | 348° |
| Radians | π/15 ≈ 0.20944 |
| Gradians | 13.3333 grad |
| Fraction of a turn | one thirtieth (1/30) (3.33%) |
| Degrees, minutes, seconds | 12° 0′ 0″ |
| Slope (grade) | 21.26% |
| Roof pitch | 2.55/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 12°
| Function | Value |
|---|---|
| sin 12° | 0.207912 |
| cos 12° | 0.978148 |
| tan 12° | 0.212557 |
12° on a protractor
How to draw a 12° 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 12° 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 12°.
Drawing it a 12° 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 2.13 inches (about 2 1/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 12°, because tan 12° ≈ 0.2126.
Where you see 12° angles
- Divide a circle into 30 equal slices and each slice is 12°, e.g. 30 spokes on a wheel or 30 equal pie-chart wedges.
- A 15-sided frame (15-sided polygon) is assembled with 12° miter cuts.
- A board sloped at 12° rises about 25.5 inches over a 10-foot (120-inch) run.
- 12° of latitude on Earth spans roughly 829 miles north to south.
- The Earth turns 12° on its axis in about 48 minutes.
Related angles
12° angle FAQ
What type of angle is 12°?
A 12° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 12°?
The complement of 12° is 78° (together they make 90°), and the supplement is 168° (together they make 180°).
How many radians is 12 degrees?
12° = π/15 radians ≈ 0.2094 rad. To convert degrees to radians, multiply by π/180: 12 × π/180 = π/15.
What is 12° as a slope or roof pitch?
12° is a 21.3% slope, which is a roof pitch of 2.55/12 (a rise of about 2 1/2 inches for every 12 inches of run).
