A 23° angle is classed as acute because it measures less than 90°. It is less than half of a right angle, and its complement (the angle that makes 90° with it) is 67°.
23° is 23/360 of a full circle, or 23π/180 radians. If you face north and turn 23° clockwise, you end up facing between NNE and NE (closest to north-northeast (NNE)).
23° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 67° |
| Supplement (adds to 180°) | 157° |
| Explement (adds to 360°) | 337° |
| Radians | 23π/180 ≈ 0.401426 |
| Gradians | 25.5556 grad |
| Fraction of a turn | 23/360 (6.39%) |
| Degrees, minutes, seconds | 23° 0′ 0″ |
| Slope (grade) | 42.45% |
| Roof pitch | 5.09/12 |
| Compass bearing | between NNE and NE (closest to north-northeast (NNE)) |
Trigonometric values of 23°
| Function | Value |
|---|---|
| sin 23° | 0.390731 |
| cos 23° | 0.920505 |
| tan 23° | 0.424475 |
23° on a protractor
How to draw a 23° 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 23° 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 23°.
Drawing it a 23° 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 4.24 inches (about 4 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 23°, because tan 23° ≈ 0.4245.
Where you see 23° angles
- Earth's axis is tilted about 23.4° relative to its orbit, and that tilt is what causes the seasons.
- A 5/12 roof pitch is 22.62°, very close to 23°.
- A board sloped at 23° rises about 50.9 inches over a 10-foot (120-inch) run.
- 23° of latitude on Earth spans roughly 1,588 miles north to south.
- The Earth turns 23° on its axis in about 1 h 32 min.
Related angles
23° angle FAQ
What type of angle is 23°?
A 23° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 23°?
The complement of 23° is 67° (together they make 90°), and the supplement is 157° (together they make 180°).
How many radians is 23 degrees?
23° = 23π/180 radians ≈ 0.4014 rad. To convert degrees to radians, multiply by π/180: 23 × π/180 = 23π/180.
What is 23° as a slope or roof pitch?
23° is a 42.4% slope, which is a roof pitch of 5.09/12 (a rise of about 5 1/8 inches for every 12 inches of run).
