A 90° angle is a right angle, the "square corner" you find on paper, tiles, door frames and boxes. The two arms are perpendicular to each other, and the angle is usually marked with a small square instead of an arc.
90° is one quarter (1/4) of a full circle, or π/2 radians. The minute hand of a clock sweeps 90° in 15 minutes. If you face north and turn 90° clockwise, you end up facing due east (E).
90° angle facts
| Angle type | Right angle (exactly 90°) |
|---|---|
| Supplement (adds to 180°) | 90° |
| Explement (adds to 360°) | 270° |
| Radians | π/2 ≈ 1.570796 |
| Gradians | 100 grad |
| Fraction of a turn | one quarter (1/4) (25%) |
| Degrees, minutes, seconds | 90° 0′ 0″ |
| Compass bearing | east (E) |
Trigonometric values of 90°
| Function | Value |
|---|---|
| sin 90° | 1 |
| cos 90° | 0 |
| tan 90° | undefined |
90° on a protractor
How to draw a 90° angle with a protractor
- Draw a straight line with a ruler. This is the first arm; mark the vertex at one end.
- Place the center mark of the protractor exactly on the vertex and line up the 0° baseline with your line.
- Find 90° on the row of numbers that reads 0° on your line (protractors have two rows running in opposite directions) and make a small dot at the edge.
- Remove the protractor and draw a line from the vertex through the dot. Mark the angle with a small square and label it 90°.
Drawing it a 90° angle without a protractor (compass and ruler)
- Construct a perpendicular line (draw arcs from two points on the line and join their crossing points).
- No compass? Fold a sheet of paper in half, then in half again the other way: the folded corner is exactly 90°.
Where you see 90° angles
- The corner of a sheet of paper, a door frame and a carpenter's square are all 90°.
- At 3:00 the hands of a clock form a right angle.
- Walls meet floors at 90° when they are plumb.
- Each interior corner of a regular square measures 90°.
- Divide a circle into 4 equal slices and each slice is 90°, e.g. 4 spokes on a wheel or 4 equal pie-chart wedges.
- 90° of latitude on Earth spans roughly 6,215 miles north to south.
- The Earth turns 90° on its axis in about 6 hours.
Related angles
90° angle FAQ
What type of angle is 90°?
A 90° angle is a right angle, because it is exactly 90°.
What is the supplement of 90°?
The supplement of 90° is 90°, because 90° + 90° = 180°. A right angle has a complement of 0°, and its supplement is another right angle.
How many radians is 90 degrees?
90° = π/2 radians ≈ 1.5708 rad. To convert degrees to radians, multiply by π/180: 90 × π/180 = π/2.
How do I measure a 90° angle on my screen?
Open the online protractor with 90° preset, or type 90 into its "Type an angle" box. You can then drag the arms onto your own lines to compare.