A 21° 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 69°.
21° is 7/120 of a full circle, or 7π/60 radians. If you face north and turn 21° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
21° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 69° |
| Supplement (adds to 180°) | 159° |
| Explement (adds to 360°) | 339° |
| Radians | 7π/60 ≈ 0.366519 |
| Gradians | 23.3333 grad |
| Fraction of a turn | 7/120 (5.83%) |
| Degrees, minutes, seconds | 21° 0′ 0″ |
| Slope (grade) | 38.39% |
| Roof pitch | 4.61/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 21°
| Function | Value |
|---|---|
| sin 21° | 0.358368 |
| cos 21° | 0.93358 |
| tan 21° | 0.383864 |
21° on a protractor
How to draw a 21° 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 21° 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 21°.
Drawing it a 21° 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 3.84 inches (about 3 13/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 21°, because tan 21° ≈ 0.3839.
Where you see 21° angles
- A board sloped at 21° rises about 46.1 inches over a 10-foot (120-inch) run.
- 21° of latitude on Earth spans roughly 1,450 miles north to south.
- The Earth turns 21° on its axis in about 1 h 24 min.
- Narrow acute angles like 21° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
21° angle FAQ
What type of angle is 21°?
A 21° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 21°?
The complement of 21° is 69° (together they make 90°), and the supplement is 159° (together they make 180°).
How many radians is 21 degrees?
21° = 7π/60 radians ≈ 0.3665 rad. To convert degrees to radians, multiply by π/180: 21 × π/180 = 7π/60.
What is 21° as a slope or roof pitch?
21° is a 38.4% slope, which is a roof pitch of 4.61/12 (a rise of about 4 5/8 inches for every 12 inches of run).
