A 60° angle is an acute angle: it is smaller than a right angle (90°). It is more than half of a right angle. Add 30° more and you get a square corner.
60° is one sixth (1/6) of a full circle, or π/3 radians. The minute hand of a clock sweeps 60° in 10 minutes. If you face north and turn 60° clockwise, you end up facing between NE and ENE (closest to east-northeast (ENE)).
60° angle facts
| Angle type | Acute angle (between 0° and 90°) |
|---|---|
| Complement (adds to 90°) | 30° |
| Supplement (adds to 180°) | 120° |
| Explement (adds to 360°) | 300° |
| Radians | π/3 ≈ 1.047198 |
| Gradians | 66.6667 grad |
| Fraction of a turn | one sixth (1/6) (16.67%) |
| Degrees, minutes, seconds | 60° 0′ 0″ |
| Slope (grade) | 173.21% |
| Roof pitch | 20.78/12 |
| Compass bearing | between NE and ENE (closest to east-northeast (ENE)) |
Trigonometric values of 60°
| Function | Value |
|---|---|
| sin 60° | √3/2 ≈ 0.866025 |
| cos 60° | 1/2 ≈ 0.5 |
| tan 60° | √3 ≈ 1.732051 |
60° on a protractor
How to draw a 60° 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 60° 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 60°.
Drawing it a 60° angle without a protractor (compass and ruler)
- Construct an equilateral triangle: with the compass set to the length of the base line, draw arcs from both ends; the crossing point makes a 60° angle with the base.
Where you see 60° angles
- Each corner of an equilateral triangle measures 60°.
- At 2:00 the hands of a clock form a 60° angle.
- Lob wedges in golf usually have about 60° of loft.
- Each interior corner of a regular triangle measures 60°.
- Divide a circle into 6 equal slices and each slice is 60°, e.g. 6 spokes on a wheel or 6 equal pie-chart wedges.
- A 3-sided frame (triangle) is assembled with 60° miter cuts.
- A 21/12 roof pitch is 60.26°, very close to 60°.
Related angles
60° angle FAQ
What type of angle is 60°?
A 60° angle is an acute angle, because it is between 0° and 90°.
What are the complement and supplement of 60°?
The complement of 60° is 30° (together they make 90°), and the supplement is 120° (together they make 180°).
How many radians is 60 degrees?
60° = π/3 radians ≈ 1.0472 rad. To convert degrees to radians, multiply by π/180: 60 × π/180 = π/3.
What is 60° as a slope or roof pitch?
60° is a 173.2% slope, which is a roof pitch of 20.78/12 (a rise of about 20 3/4 inches for every 12 inches of run).