A 54° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 36° more and you get a square corner.
54° is 3/20 of a full circle, or 3π/10 radians. The minute hand of a clock sweeps 54° in 9 minutes. If you face north and turn 54° clockwise, you end up facing between NE and ENE (closest to northeast (NE)).
54° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 36° |
| Supplement (adds to 180°) | 126° |
| Explement (adds to 360°) | 306° |
| Radians | 3π/10 ≈ 0.942478 |
| Gradians | 60 grad |
| Fraction of a turn | 3/20 (15%) |
| Degrees, minutes, seconds | 54° 0′ 0″ |
| Slope (grade) | 137.64% |
| Roof pitch | 16.52/12 |
| Compass bearing | between NE and ENE (closest to northeast (NE)) |
Trigonometric values of 54°
| Function | Value |
|---|---|
| sin 54° | (√5 + 1)/4 ≈ 0.809017 |
| cos 54° | √(10 − 2√5)/4 ≈ 0.587785 |
| tan 54° | 1.376382 |
54° on a protractor
How to draw a 54° 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 54° 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 54°.
Drawing it a 54° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 7.27 inches (about 7 1/4″) along it from the vertex.
- At that mark, draw a line straight up at 90° and measure exactly 10 inches up it.
- Join the top mark to the vertex. The angle at the vertex is 54°, because tan 54° ≈ 1.3764.
Where you see 54° angles
- A board sloped at 54° rises about 165.2 inches over a 10-foot (120-inch) run.
- 54° of latitude on Earth spans roughly 3,729 miles north to south.
- The Earth turns 54° on its axis in about 3 h 36 min.
- Narrow acute angles like 54° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
54° angle FAQ
What type of angle is 54°?
A 54° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 54°?
The complement of 54° is 36° (together they make 90°), and the supplement is 126° (together they make 180°).
How many radians is 54 degrees?
54° = 3π/10 radians ≈ 0.9425 rad. To convert degrees to radians, multiply by π/180: 54 × π/180 = 3π/10.
What is 54° as a slope or roof pitch?
54° is a 137.6% slope, which is a roof pitch of 16.52/12 (a rise of about 16 1/2 inches for every 12 inches of run).
