A 3° angle is an acute angle: it is smaller than a right angle (90°). It is a very narrow angle, just 3.3% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
3° is one one hundred twentieth (1/120) of a full circle, or π/60 radians. If you face north and turn 3° clockwise, you end up facing between N and NNE (closest to north (N)).
3° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 87° |
| Supplement (adds to 180°) | 177° |
| Explement (adds to 360°) | 357° |
| Radians | π/60 ≈ 0.05236 |
| Gradians | 3.3333 grad |
| Fraction of a turn | one one hundred twentieth (1/120) (0.83%) |
| Degrees, minutes, seconds | 3° 0′ 0″ |
| Slope (grade) | 5.24% |
| Roof pitch | 0.63/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 3°
| Function | Value |
|---|---|
| sin 3° | 0.052336 |
| cos 3° | 0.99863 |
| tan 3° | 0.052408 |
3° on a protractor
How to draw a 3° 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 3° 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 3°.
Drawing it a 3° 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 0.52 inches (about 1/2″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 3°, because tan 3° ≈ 0.0524.
Where you see 3° angles
- Divide a circle into 120 equal slices and each slice is 3°, e.g. 120 spokes on a wheel or 120 equal pie-chart wedges.
- A board sloped at 3° rises about 6.3 inches over a 10-foot (120-inch) run.
- 3° of latitude on Earth spans roughly 207 miles north to south.
- The Earth turns 3° on its axis in about 12 minutes.
Related angles
3° angle FAQ
What type of angle is 3°?
A 3° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 3°?
The complement of 3° is 87° (together they make 90°), and the supplement is 177° (together they make 180°).
How many radians is 3 degrees?
3° = π/60 radians ≈ 0.0524 rad. To convert degrees to radians, multiply by π/180: 3 × π/180 = π/60.
What is 3° as a slope or roof pitch?
3° is a 5.2% slope, which is a roof pitch of 0.63/12 (a rise of about 5/8 inches for every 12 inches of run).
