At 7°, this angle is acute, meaning it is narrower than the corner of a square. It is a very narrow angle, just 7.8% of a right angle, the kind of small slope you see in drainage, ramps and fine adjustments.
7° is 7/360 of a full circle, or 7π/180 radians. If you face north and turn 7° clockwise, you end up facing between N and NNE (closest to north (N)).
7° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 83° |
| Supplement (adds to 180°) | 173° |
| Explement (adds to 360°) | 353° |
| Radians | 7π/180 ≈ 0.122173 |
| Gradians | 7.7778 grad |
| Fraction of a turn | 7/360 (1.94%) |
| Degrees, minutes, seconds | 7° 0′ 0″ |
| Slope (grade) | 12.28% |
| Roof pitch | 1.47/12 |
| Compass bearing | between N and NNE (closest to north (N)) |
Trigonometric values of 7°
| Function | Value |
|---|---|
| sin 7° | 0.121869 |
| cos 7° | 0.992546 |
| tan 7° | 0.122785 |
7° on a protractor
How to draw a 7° 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 7° 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 7°.
Drawing it a 7° 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 1.23 inches (about 1 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 7°, because tan 7° ≈ 0.1228.
Where you see 7° angles
- The 1:8 dovetail slope often recommended for hardwoods is about 7.1°.
- A board sloped at 7° rises about 14.7 inches over a 10-foot (120-inch) run.
- 7° of latitude on Earth spans roughly 483 miles north to south.
- The Earth turns 7° on its axis in about 28 minutes.
Related angles
7° angle FAQ
What type of angle is 7°?
A 7° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 7°?
The complement of 7° is 83° (together they make 90°), and the supplement is 173° (together they make 180°).
How many radians is 7 degrees?
7° = 7π/180 radians ≈ 0.1222 rad. To convert degrees to radians, multiply by π/180: 7 × π/180 = 7π/180.
What is 7° as a slope or roof pitch?
7° is a 12.3% slope, which is a roof pitch of 1.47/12 (a rise of about 1 1/2 inches for every 12 inches of run).
