A 5° angle is classed as acute because it measures less than 90°. It is a very narrow angle, just 5.6% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
5° is one seventy-second (1/72) of a full circle, or π/36 radians. If you face north and turn 5° clockwise, you end up facing between N and NNE (closest to north (N)).
5° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 85° |
| Supplement (adds to 180°) | 175° |
| Explement (adds to 360°) | 355° |
| Radians | π/36 ≈ 0.087266 |
| Gradians | 5.5556 grad |
| Fraction of a turn | one seventy-second (1/72) (1.39%) |
| Degrees, minutes, seconds | 5° 0′ 0″ |
| Slope (grade) | 8.75% |
| Roof pitch | 1.05/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 5°
| Function | Value |
|---|---|
| sin 5° | 0.087156 |
| cos 5° | 0.996195 |
| tan 5° | 0.087489 |
5° on a protractor
How to draw a 5° 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 5° 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 5°.
Drawing it a 5° 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 0.87 inches (about 7/8″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 5°, because tan 5° ≈ 0.0875.
Where you see 5° angles
- The ADA limits wheelchair ramps to a 1:12 slope, about 4.8°. A 5° ramp is slightly too steep to meet that rule.
- Divide a circle into 72 equal slices and each slice is 5°, e.g. 72 spokes on a wheel or 72 equal pie-chart wedges.
- A 36-sided frame (36-sided polygon) is assembled with 5° miter cuts.
- A 1/12 roof pitch is 4.76°, very close to 5°.
- A board sloped at 5° rises about 10.5 inches over a 10-foot (120-inch) run.
- 5° of latitude on Earth spans roughly 345 miles north to south.
- The Earth turns 5° on its axis in about 20 minutes.
Related angles
5° angle FAQ
What type of angle is 5°?
A 5° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 5°?
The complement of 5° is 85° (together they make 90°), and the supplement is 175° (together they make 180°).
How many radians is 5 degrees?
5° = π/36 radians ≈ 0.0873 rad. To convert degrees to radians, multiply by π/180: 5 × π/180 = π/36.
What is 5° as a slope or roof pitch?
5° is a 8.7% slope, which is a roof pitch of 1.05/12 (a rise of about 1 inches for every 12 inches of run).
