A 63° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 27° more and you get a square corner.
63° is 7/40 of a full circle, or 7π/20 radians. If you face north and turn 63° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
63° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 27° |
| Supplement (adds to 180°) | 117° |
| Explement (adds to 360°) | 297° |
| Radians | 7π/20 ≈ 1.099557 |
| Gradians | 70 grad |
| Fraction of a turn | 7/40 (17.5%) |
| Degrees, minutes, seconds | 63° 0′ 0″ |
| Slope (grade) | 196.26% |
| Roof pitch | 23.55/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 63°
| Function | Value |
|---|---|
| sin 63° | 0.891007 |
| cos 63° | 0.45399 |
| tan 63° | 1.962611 |
63° on a protractor
How to draw a 63° 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 63° 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 63°.
Drawing it a 63° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 5.1 inches (about 5 1/8″) 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 63°, because tan 63° ≈ 1.9626.
Where you see 63° angles
- A 24/12 roof pitch is 63.43°, very close to 63°.
- 63° of latitude on Earth spans roughly 4,350 miles north to south.
- The Earth turns 63° on its axis in about 4 h 12 min.
- Narrow acute angles like 63° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
63° angle FAQ
What type of angle is 63°?
A 63° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 63°?
The complement of 63° is 27° (together they make 90°), and the supplement is 117° (together they make 180°).
How many radians is 63 degrees?
63° = 7π/20 radians ≈ 1.0996 rad. To convert degrees to radians, multiply by π/180: 63 × π/180 = 7π/20.
What is 63° as a slope or roof pitch?
63° is a 196.3% slope, which is a roof pitch of 23.55/12 (a rise of about 23 1/2 inches for every 12 inches of run).
