At 301°, this is a reflex angle, which goes more than halfway around a circle. It is the "outside" of a 59° angle: together they make a full 360° circle.
301° is 301/360 of a full circle, or 301π/180 radians. If you face north and turn 301° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
301° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 59° |
| Radians | 301π/180 ≈ 5.253441 |
| Gradians | 334.4444 grad |
| Fraction of a turn | 301/360 (83.61%) |
| Degrees, minutes, seconds | 301° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 301°
| Function | Value |
|---|---|
| sin 301° | −0.857167 |
| cos 301° | 0.515038 |
| tan 301° | −1.664279 |
301° on a protractor
How to draw a 301° angle with a protractor
- Subtract from 360°: 360° − 301° = 59°. 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 59°.
- Join the vertex to the dot. The inside angle is 59°; the outside angle, going the long way around, is 301°. Draw the angle arc on the outside and label it 301°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 301° directly.
Drawing it a 301° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.01 inches (about 6″) 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 59°, because tan 59° ≈ 1.6643.
- That gives you 59°. The outside (reflex) angle is 301°.
Where you see 301° angles
- The Earth turns 301° on its axis in about 20 h 4 min.
- A 301° 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
301° angle FAQ
What type of angle is 301°?
A 301° angle is a reflex angle, because it is between 180° and 360°.
Does a 301° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 301° is already larger than both. What it does have is an explement (conjugate) of 59°, the angle that completes a full 360° circle.
How many radians is 301 degrees?
301° = 301π/180 radians ≈ 5.2534 rad. To convert degrees to radians, multiply by π/180: 301 × π/180 = 301π/180.
How do I measure a 301° angle on my screen?
Open the online protractor with 301° preset, or type 301 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
