An 18° angle is an acute angle: it is smaller than a right angle (90°). It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 72°.
18° is one twentieth (1/20) of a full circle, or π/10 radians. The minute hand of a clock sweeps 18° in 3 minutes. If you face north and turn 18° clockwise, you end up facing between N and NNE (closest to north-northeast (NNE)).
18° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 72° |
| Supplement (adds to 180°) | 162° |
| Explement (adds to 360°) | 342° |
| Radians | π/10 ≈ 0.314159 |
| Gradians | 20 grad |
| Fraction of a turn | one twentieth (1/20) (5%) |
| Degrees, minutes, seconds | 18° 0′ 0″ |
| Slope (grade) | 32.49% |
| Roof pitch | 3.9/12 |
| Compass bearing | between N and NNE (closest to north-northeast (NNE)) |
Trigonometric values of 18°
| Function | Value |
|---|---|
| sin 18° | (√5 − 1)/4 ≈ 0.309017 |
| cos 18° | √(10 + 2√5)/4 ≈ 0.951057 |
| tan 18° | 0.32492 |
18° on a protractor
How to draw an 18° 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 18° 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 18°.
Drawing it an 18° 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 3.25 inches (about 3 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 18°, because tan 18° ≈ 0.3249.
Where you see 18° angles
- Divide a circle into 20 equal slices and each slice is 18°, e.g. 20 spokes on a wheel or 20 equal pie-chart wedges.
- A 10-sided frame (decagon) is assembled with 18° miter cuts.
- A 4/12 roof pitch is 18.43°, very close to 18°.
- A board sloped at 18° rises about 39 inches over a 10-foot (120-inch) run.
- 18° of latitude on Earth spans roughly 1,243 miles north to south.
- The Earth turns 18° on its axis in about 1 h 12 min.
Related angles
18° angle FAQ
What type of angle is 18°?
An 18° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 18°?
The complement of 18° is 72° (together they make 90°), and the supplement is 162° (together they make 180°).
How many radians is 18 degrees?
18° = π/10 radians ≈ 0.3142 rad. To convert degrees to radians, multiply by π/180: 18 × π/180 = π/10.
What is 18° as a slope or roof pitch?
18° is a 32.5% slope, which is a roof pitch of 3.9/12 (a rise of about 3 7/8 inches for every 12 inches of run).
