At 13°, this angle is acute, meaning it is narrower than the corner of a square. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 77°.
13° is 13/360 of a full circle, or 13π/180 radians. If you face north and turn 13° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
13° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 77° |
| Supplement (adds to 180°) | 167° |
| Explement (adds to 360°) | 347° |
| Radians | 13π/180 ≈ 0.226893 |
| Gradians | 14.4444 grad |
| Fraction of a turn | 13/360 (3.61%) |
| Degrees, minutes, seconds | 13° 0′ 0″ |
| Slope (grade) | 23.09% |
| Roof pitch | 2.77/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 13°
| Function | Value |
|---|---|
| sin 13° | 0.224951 |
| cos 13° | 0.97437 |
| tan 13° | 0.230868 |
13° on a protractor
How to draw a 13° 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 13° 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 13°.
Drawing it a 13° 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 2.31 inches (about 2 5/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 13°, because tan 13° ≈ 0.2309.
Where you see 13° angles
- A board sloped at 13° rises about 27.7 inches over a 10-foot (120-inch) run.
- 13° of latitude on Earth spans roughly 898 miles north to south.
- The Earth turns 13° on its axis in about 52 minutes.
- Narrow acute angles like 13° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
13° angle FAQ
What type of angle is 13°?
A 13° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 13°?
The complement of 13° is 77° (together they make 90°), and the supplement is 167° (together they make 180°).
How many radians is 13 degrees?
13° = 13π/180 radians ≈ 0.2269 rad. To convert degrees to radians, multiply by π/180: 13 × π/180 = 13π/180.
What is 13° as a slope or roof pitch?
13° is a 23.1% slope, which is a roof pitch of 2.77/12 (a rise of about 2 3/4 inches for every 12 inches of run).
