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.

A protractor measuring a 50 degree angle0180101702016030150401405013060120701108010090901008011070120601305014040150301602017010180050°
The center mark sits on the vertex, the baseline lies on one arm, and the other arm points to 50°.

What you need

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

  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. 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

  1. Draw a straight line with a ruler. This is the first arm. Mark a dot at one end for the vertex.
  2. Place the protractor's center mark on the dot and line the baseline up with your line.
  3. 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.
  4. Remove the protractor and use the ruler to join the vertex to the tick mark.
  5. 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.

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