A 2° angle is classed as acute because it measures less than 90°. It is a very narrow angle, just 2.2% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
2° is one one hundred eightieth (1/180) of a full circle, or π/90 radians. If you face north and turn 2° clockwise, you end up facing between N and NNE (closest to north (N)).
2° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 88° |
| Supplement (adds to 180°) | 178° |
| Explement (adds to 360°) | 358° |
| Radians | π/90 ≈ 0.034907 |
| Gradians | 2.2222 grad |
| Fraction of a turn | one one hundred eightieth (1/180) (0.56%) |
| Degrees, minutes, seconds | 2° 0′ 0″ |
| Slope (grade) | 3.49% |
| Roof pitch | 0.42/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 2°
| Function | Value |
|---|---|
| sin 2° | 0.034899 |
| cos 2° | 0.999391 |
| tan 2° | 0.034921 |
2° on a protractor
How to draw a 2° 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 2° 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 2°.
Drawing it a 2° 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 0.35 inches (about 3/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 2°, because tan 2° ≈ 0.0349.
Where you see 2° angles
- A board sloped at 2° rises about 4.2 inches over a 10-foot (120-inch) run.
- 2° of latitude on Earth spans roughly 138 miles north to south.
- The Earth turns 2° on its axis in about 8 minutes.
- Narrow acute angles like 2° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
2° angle FAQ
What type of angle is 2°?
A 2° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 2°?
The complement of 2° is 88° (together they make 90°), and the supplement is 178° (together they make 180°).
How many radians is 2 degrees?
2° = π/90 radians ≈ 0.0349 rad. To convert degrees to radians, multiply by π/180: 2 × π/180 = π/90.
What is 2° as a slope or roof pitch?
2° is a 3.5% slope, which is a roof pitch of 0.42/12 (a rise of about 3/8 inches for every 12 inches of run).
