A 324° 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 36° angle: together they make a full 360° circle.
324° is 9/10 of a full circle, or 9π/5 radians. The minute hand of a clock sweeps 324° in 54 minutes. If you face north and turn 324° clockwise, you end up facing between NW and NNW (closest to northwest (NW)).
324° angle facts
| Angle type | Reflex angle (between 180° and 360°) |
|---|---|
| Explement (adds to 360°) | 36° |
| Radians | 9π/5 ≈ 5.654867 |
| Gradians | 360 grad |
| Fraction of a turn | 9/10 (90%) |
| Degrees, minutes, seconds | 324° 0′ 0″ |
| Compass bearing | between NW and NNW (closest to northwest (NW)) |
Trigonometric values of 324°
| Function | Value |
|---|---|
| sin 324° | −√(10 − 2√5)/4 ≈ −0.587785 |
| cos 324° | (√5 + 1)/4 ≈ 0.809017 |
| tan 324° | −0.726543 |
324° on a protractor
How to draw a 324° angle with a protractor
- Subtract from 360°: 360° − 324° = 36°. 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 36°.
- Join the vertex to the dot. The inside angle is 36°; the outside angle, going the long way around, is 324°. Draw the angle arc on the outside and label it 324°.
- With a 360° protractor you can skip the subtraction: put 0° on your first line and mark 324° directly.
Drawing it a 324° 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 7.27 inches (about 7 1/4″) up that line and make a mark.
- Join the mark to the vertex. The angle at the vertex is 36°, because tan 36° ≈ 0.7265.
- That gives you 36°. The outside (reflex) angle is 324°.
Where you see 324° angles
- The Earth turns 324° on its axis in about 21 h 36 min.
- A 324° 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
324° angle FAQ
What type of angle is 324°?
A 324° angle is a reflex angle, because it is between 180° and 360°.
Does a 324° angle have a complement or supplement?
No. Complements add up to 90° and supplements to 180°, and 324° is already larger than both. What it does have is an explement (conjugate) of 36°, the angle that completes a full 360° circle.
How many radians is 324 degrees?
324° = 9π/5 radians ≈ 5.6549 rad. To convert degrees to radians, multiply by π/180: 324 × π/180 = 9π/5.
How do I measure a 324° angle on my screen?
Open the online protractor with 324° preset, or type 324 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.
