A 303° 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 57° angle: together they make a full 360° circle.
303° is 101/120 of a full circle, or 101π/60 radians. If you face north and turn 303° clockwise, you end up facing between WNW and NW (closest to west-northwest (WNW)).
303° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 57° |
| Radians | 101π/60 ≈ 5.288348 |
| Gradians | 336.6667 grad |
| Fraction of a turn | 101/120 (84.17%) |
| Degrees, minutes, seconds | 303° 0′ 0″ |
| Compass bearing | between WNW and NW (closest to west-northwest (WNW)) |
Trigonometric values of 303°
| Function | Value |
|---|---|
| sin 303° | −0.838671 |
| cos 303° | 0.544639 |
| tan 303° | −1.539865 |
303° on a protractor
How to draw a 303° angle with a protractor
- Subtract from 360°: 360° − 303° = 57°. 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 57°.
- Join the vertex to the dot. The inside angle is 57°; the outside angle, going the long way around, is 303°. Draw the angle arc on the outside and label it 303°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 303° directly.
Drawing it a 303° angle without a protractor (rise and run method)
- Draw a straight baseline and measure 6.49 inches (about 6 1/2″) 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 57°, because tan 57° ≈ 1.5399.
- That gives you 57°. The outside (reflex) angle is 303°.
Where you see 303° angles
- The Earth turns 303° on its axis in about 20 h 12 min.
- A 303° 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
303° angle FAQ
What type of angle is 303°?
A 303° angle is a reflex angle, because it is between 180° and 360°.
Does a 303° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 303° is already larger than both. What it does have is an explement (conjugate) of 57°, the angle that completes a full 360° circle.
How many radians is 303 degrees?
303° = 101π/60 radians ≈ 5.2883 rad. To convert degrees to radians, multiply by π/180: 303 × π/180 = 101π/60.
How do I measure a 303° angle on my screen?
Open the online protractor with 303° preset, or type 303 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
