A 240° angle is a reflex angle: it is bigger than a straight line (180°) but less than a full turn (360°). It is the "outside" of a 120° angle: together they make a full 360° circle.
240° is two thirds (2/3) of a full circle, or 4π/3 radians. The minute hand of a clock sweeps 240° in 40 minutes. If you face north and turn 240° clockwise, you end up facing between SW and WSW (closest to west-southwest (WSW)).
240° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 120° |
| Radians | 4π/3 ≈ 4.18879 |
| Gradians | 266.6667 grad |
| Fraction of a turn | two thirds (2/3) (66.67%) |
| Degrees, minutes, seconds | 240° 0′ 0″ |
| Compass bearing | between SW and WSW (closest to west-southwest (WSW)) |
Trigonometric values of 240°
| Function | Value |
|---|---|
| sin 240° | −√3/2 ≈ −0.866025 |
| cos 240° | −1/2 ≈ −0.5 |
| tan 240° | √3 ≈ 1.732051 |
240° on a protractor
How to draw a 240° angle with a protractor
- Subtract from 360°: 360° − 240° = 120°. A standard protractor only goes to 180°, so you draw the smaller angle first.
- Draw a straight line with a ruler and mark the vertex at one end.
- Place the protractor's center mark on the vertex, line up the 0° baseline with your line, and make a dot at 120°.
- Join the vertex to the dot. The inside angle is 120°; the outside angle, going the long way around, is 240°. Draw the angle arc on the outside and label it 240°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 240° directly.
Drawing it a 240° angle without a protractor (compass and ruler)
- Draw a 180° angle: draw a straight line.
- Inside it, starting from the second arm, mark a 60° angle: 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.
- What is left between the first arm and the new line is 180° − 60° = 120°.
- That gives you 120°. The reflex angle on the outside of it is 240°.
Where you see 240° angles
- The Earth turns 240° on its axis in about 16 hours.
- A 240° reflex angle is what you measure when you go the "long way" around, like the outside corner of a building or a turn of more than half a circle.
Related angles
240° angle FAQ
What type of angle is 240°?
A 240° angle is a reflex angle, because it is between 180° and 360°.
Does a 240° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 240° is already larger than both. What it does have is an explement (conjugate) of 120°, the angle that completes a full 360° circle.
How many radians is 240 degrees?
240° = 4π/3 radians ≈ 4.1888 rad. To convert degrees to radians, multiply by π/180: 240 × π/180 = 4π/3.
How do I measure a 240° angle on my screen?
Open the online protractor with 240° preset, or type 240 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
