A 300° 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 60° angle: together they make a full 360° circle.
300° is 5/6 of a full circle, or 5π/3 radians. The minute hand of a clock sweeps 300° in 50 minutes. If you face north and turn 300° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
300° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 60° |
| Radians | 5π/3 ≈ 5.235988 |
| Gradians | 333.3333 grad |
| Fraction of a turn | 5/6 (83.33%) |
| Degrees, minutes, seconds | 300° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 300°
| Function | Value |
|---|---|
| sin 300° | −√3/2 ≈ −0.866025 |
| cos 300° | 1/2 ≈ 0.5 |
| tan 300° | −√3 ≈ −1.732051 |
300° on a protractor
How to draw a 300° angle with a protractor
- Subtract from 360°: 360° − 300° = 60°. 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 60°.
- Join the vertex to the dot. The inside angle is 60°; the outside angle, going the long way around, is 300°. Draw the angle arc on the outside and label it 300°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 300° directly.
Drawing it a 300° 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.
- That gives you 60°. The reflex angle on the outside of it is 300°.
Where you see 300° angles
- The Earth turns 300° on its axis in about 20 hours.
- A 300° 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
300° angle FAQ
What type of angle is 300°?
A 300° angle is a reflex angle, because it is between 180° and 360°.
Does a 300° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 300° is already larger than both. What it does have is an explement (conjugate) of 60°, the angle that completes a full 360° circle.
How many radians is 300 degrees?
300° = 5π/3 radians ≈ 5.236 rad. To convert degrees to radians, multiply by π/180: 300 × π/180 = 5π/3.
How do I measure a 300° angle on my screen?
Open the online protractor with 300° preset, or type 300 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
