At 61°, this angle is acute, meaning it is narrower than the corner of a square. It is more than half of a right angle. Add 29° more and you get a square corner.
61° is 61/360 of a full circle, or 61π/180 radians. If you face north and turn 61° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
61° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 29° |
| Supplement (adds to 180°) | 119° |
| Explement (adds to 360°) | 299° |
| Radians | 61π/180 ≈ 1.064651 |
| Gradians | 67.7778 grad |
| Fraction of a turn | 61/360 (16.94%) |
| Degrees, minutes, seconds | 61° 0′ 0″ |
| Slope (grade) | 180.4% |
| Roof pitch | 21.65/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 61°
| Function | Value |
|---|---|
| sin 61° | 0.87462 |
| cos 61° | 0.48481 |
| tan 61° | 1.804048 |
61° on a protractor
How to draw a 61° 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 61° 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 61°.
Drawing it a 61° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 5.54 inches (about 5 9/16″) 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 61°, because tan 61° ≈ 1.804.
Where you see 61° angles
- A 22/12 roof pitch is 61.39°, very close to 61°.
- 61° of latitude on Earth spans roughly 4,212 miles north to south.
- The Earth turns 61° on its axis in about 4 h 4 min.
- Narrow acute angles like 61° show up in ramps, roof slopes, scissors blades, the tip of a pencil and the V of a flying flock of birds.
Related angles
61° angle FAQ
What type of angle is 61°?
A 61° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 61°?
The complement of 61° is 29° (together they make 90°), and the supplement is 119° (together they make 180°).
How many radians is 61 degrees?
61° = 61π/180 radians ≈ 1.0647 rad. To convert degrees to radians, multiply by π/180: 61 × π/180 = 61π/180.
What is 61° as a slope or roof pitch?
61° is a 180.4% slope, which is a roof pitch of 21.65/12 (a rise of about 21 5/8 inches for every 12 inches of run).
