A 354° 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 6° angle: together they make a full 360° circle.
354° is 59/60 of a full circle, or 59π/30 radians. The minute hand of a clock sweeps 354° in 59 minutes. If you face north and turn 354° clockwise, you end up facing between NNW and N (closest to north (N)).
354° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 6° |
| Radians | 59π/30 ≈ 6.178466 |
| Gradians | 393.3333 grad |
| Fraction of a turn | 59/60 (98.33%) |
| Degrees, minutes, seconds | 354° 0′ 0″ |
| Compass bearing | between NNW and N (closest to north (N)) |
Trigonometric values of 354°
| Function | Value |
|---|---|
| sin 354° | −0.104528 |
| cos 354° | 0.994522 |
| tan 354° | −0.105104 |
354° on a protractor
How to draw a 354° angle with a protractor
- Subtract from 360°: 360° − 354° = 6°. 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 6°.
- Join the vertex to the dot. The inside angle is 6°; the outside angle, going the long way around, is 354°. Draw the angle arc on the outside and label it 354°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 354° directly.
Drawing it a 354° angle without a protractor (rise and run method)
- Draw a straight baseline and measure exactly 10 inches along it from the vertex.
- At the 10-inch mark, draw a short line straight up at 90° (use a carpenter's square or the corner of a sheet of paper).
- Measure 1.05 inches (about 1 1/16″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 6°, because tan 6° ≈ 0.1051.
- That gives you 6°. The outside (reflex) angle is 354°.
Where you see 354° angles
- The Earth turns 354° on its axis in about 23 h 36 min.
- A 354° 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
354° angle FAQ
What type of angle is 354°?
A 354° angle is a reflex angle, because it is between 180° and 360°.
Does a 354° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 354° is already larger than both. What it does have is an explement (conjugate) of 6°, the angle that completes a full 360° circle.
How many radians is 354 degrees?
354° = 59π/30 radians ≈ 6.1785 rad. To convert degrees to radians, multiply by π/180: 354 × π/180 = 59π/30.
How do I measure a 354° angle on my screen?
Open the online protractor with 354° preset, or type 354 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
