How to Use a Protractor
A protractor measures angles in degrees. Once you know where to put the center and which row of numbers to read, it takes about ten seconds.
What you need
- A protractor: a physical one, a printable protractor, or the free online protractor
- A sharp pencil
- A ruler or straightedge to extend short lines
Parts of a protractor
- Baseline: the straight line through the 0° and 180° marks. You line it up with one arm of the angle.
- Center mark (origin): the small hole, cross or dot in the middle of the baseline. It always goes on the vertex.
- Two scales: an outer and an inner row of numbers running in opposite directions, so you can measure from either side.
- Tick marks: small marks every 1°, medium marks every 5° and long marks every 10°.
For a closer look at the scales, read how to read a protractor.
How to measure an angle with a protractor
- Find the vertex. Locate the vertex, the point where the two arms of the angle meet. If the arms are short, extend them with a ruler so they reach past the protractor's numbers.
- Place the center mark on the vertex. Put the small hole, cross or dot in the middle of the protractor's straight edge exactly on the vertex.
- Line up the baseline with one arm. Rotate the protractor, keeping the center on the vertex, until the 0° line lies exactly along one arm of the angle.
- Read the scale that starts at zero. Follow the other arm to the curved edge and read the number where it crosses, using the row of numbers that starts at 0 on the arm you lined up.
- Sanity-check the answer. If the angle looks smaller than a square corner the answer must be less than 90°; if it looks wider, more than 90°. If not, you read the wrong scale.
Example (picture above): the right-hand arm lies on the baseline. The outer row of numbers reads 0° on that arm, and the other arm crosses the outer row at 50° (the inner row shows 130° at the same spot). The angle is clearly narrower than a square corner, so the answer is 50°, not 130°.
How to draw an angle with a protractor
- Draw a straight line with a ruler. This is the first arm. Mark a dot at one end for the vertex.
- Place the protractor's center mark on the dot and line the baseline up with your line.
- Find the angle you want on the scale that starts at 0° on your line, and make a small tick mark at the edge of the protractor.
- Remove the protractor and use the ruler to join the vertex to the tick mark.
- Label the angle and draw a small arc between the arms to show which angle you mean.
Want a quick visual? Every angle from 1° to 360° has its own page with a diagram and drawing steps. Try the 30° angle, 45° angle or 120° angle.
Measuring angles larger than 180°
A standard protractor is a half circle, so it stops at 180°. To measure a reflex angle (for example the outside corner of an L-shaped room), measure the smaller angle between the same two arms and subtract it from 360°. If the inside angle is 100°, the reflex angle is 260°. A full-circle 360° protractor reads it directly, and so does our online protractor when you switch Show to Reflex.
Common mistakes (and how to avoid them)
- Reading the wrong scale. This is the most common error. Always start from the 0° that sits on your first arm, and sanity-check acute vs. obtuse.
- Putting the edge, not the center mark, on the vertex. The bottom edge of many protractors is below the baseline. Use the baseline and center mark.
- Short arms. If the arm stops before the numbers, you will guess. Extend it with a ruler first.
- Parallax. Look straight down at the scale, not from the side, especially with thick protractors.
- Letting the protractor slip. Hold it down with two fingers while you read or mark.
Using a protractor on a screen
You can do everything above on your phone or computer with the online protractor: drag its center onto the vertex, drag arm A onto one line and arm B onto the other, and read the angle to 0.1°. It also works on photos (measure angle from photo) and through your camera (protractor camera).
Frequently asked questions
Which scale do I use on a protractor?
Use the row of numbers that reads 0° on the arm you lined up with the baseline. Which row that is depends on the protractor and on which way your arm points, so look for the 0 rather than memorizing "inner" or "outer". Then check: acute angles must read less than 90°.
How do I measure an angle bigger than 180° with a protractor?
Measure the smaller angle on the other side of the arms, then subtract it from 360°. For example, if the inside angle is 120°, the reflex angle is 360° − 120° = 240°. A 360° protractor or the online protractor in Reflex mode reads it directly.
What if the lines are too short to reach the numbers?
Extend both arms with a ruler and a sharp pencil before you measure. Extending the lines never changes the angle, and it makes the reading much more accurate.
How accurate is a school protractor?
A typical 6-inch plastic protractor is marked in 1° steps, so careful readings are good to about ±0.5°. Thick pencil lines, a worn center mark or parallax (looking at the scale from an angle) can add another degree of error.