A 15° 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 75°.
15° is one twenty-fourth (1/24) of a full circle, or π/12 radians. If you face north and turn 15° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
15° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 75° |
| Supplement (adds to 180°) | 165° |
| Explement (adds to 360°) | 345° |
| Radians | π/12 ≈ 0.261799 |
| Gradians | 16.6667 grad |
| Fraction of a turn | one twenty-fourth (1/24) (4.17%) |
| Degrees, minutes, seconds | 15° 0′ 0″ |
| Slope (grade) | 26.79% |
| Roof pitch | 3.22/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 15°
| Function | Value |
|---|---|
| sin 15° | (√6 − √2)/4 ≈ 0.258819 |
| cos 15° | (√6 + √2)/4 ≈ 0.965926 |
| tan 15° | 2 − √3 ≈ 0.267949 |
15° on a protractor
How to draw a 15° 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 15° 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 15°.
Drawing it a 15° angle without a protractor (compass and ruler)
- Construct a 30° angle, then bisect it.
Where you see 15° angles
- The Earth rotates 15° every hour, which is why time zones are roughly 15° of longitude wide.
- Many Japanese-style kitchen knives are sharpened at about 15° per side.
- Divide a circle into 24 equal slices and each slice is 15°, e.g. 24 spokes on a wheel or 24 equal pie-chart wedges.
- A 12-sided frame (dodecagon) is assembled with 15° miter cuts.
- A board sloped at 15° rises about 32.2 inches over a 10-foot (120-inch) run.
- 15° of latitude on Earth spans roughly 1,036 miles north to south.
- The Earth turns 15° on its axis in about 1 hour.
Related angles
15° angle FAQ
What type of angle is 15°?
A 15° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 15°?
The complement of 15° is 75° (together they make 90°), and the supplement is 165° (together they make 180°).
How many radians is 15 degrees?
15° = π/12 radians ≈ 0.2618 rad. To convert degrees to radians, multiply by π/180: 15 × π/180 = π/12.
What is 15° as a slope or roof pitch?
15° is a 26.8% slope, which is a roof pitch of 3.22/12 (a rise of about 3 1/4 inches for every 12 inches of run).