How to Read a Protractor
Two rows of numbers, 180 tiny marks: it looks confusing, but reading a protractor comes down to one rule: read the row that starts at 0 on your line.
The anatomy of a protractor scale
| Part | What it is | How to use it |
|---|---|---|
| Baseline | The straight line from 0° to 180° | Lay it along one arm of the angle |
| Center mark | The hole, cross or dot at the middle of the baseline | Always goes exactly on the vertex |
| Outer and inner scale | Two rows of numbers 0–180 running in opposite directions | Read the row that shows 0 on your base arm |
| Long ticks | Every 10°, next to a number | Count by tens |
| Medium ticks | Every 5° | Halfway between two numbers |
| Short ticks | Every 1° | Count single degrees |
How to read the scale, step by step
- Find the zero on your arm. After lining up the baseline with one arm, look at where that arm meets the curved scale. One of the two rows of numbers shows 0 there. That is the row you will read.
- Follow the same row. Move along that row, counting up 10, 20, 30… toward the second arm. Ignore the other row entirely.
- Count the small ticks. Find the last numbered (10°) mark before the second arm, then count the small 1° ticks. The medium tick halfway between numbers is 5°.
- Estimate between ticks. If the arm falls between two 1° ticks, estimate the fraction. Halfway is .5°.
- Check acute or obtuse. An angle narrower than a square corner must be under 90°; a wider one must be over 90°. If your number disagrees, you read the other row.
Inner scale or outer scale?
This is where most mistakes happen. The two rows always add up to 180°, so if you read the wrong one you get the supplement of your angle, for example 130° instead of 50°. The fix is to never think "inner" or "outer": just look at your base arm, find the row that reads 0 there, and stay on that row. On this site's protractors (the online protractor and the printable protractor) the outer row counts counter-clockwise from the right; on many school protractors it is the other way round. The rule works for all of them.
Quick check: is the angle narrower than the corner of a sheet of paper? Then the answer is less than 90°. Wider? More than 90°. If your reading disagrees, switch rows.
Worked examples
- A sharp angle opening to the right: base arm on the right, the row that reads 0 there shows 35 at the second arm → 35°.
- A wide angle opening to the left: base arm on the left, follow the row that is 0 on the left → second arm at 140 → 140° (the other row would say 40, which cannot be right for a wide angle).
- Between the ticks: the second arm sits halfway between 67 and 68 → 67.5°. That is the 67.5° angle, used in octagon construction.
- More than 180°: measure the inside angle (say 75°) and subtract from 360°: the reflex angle is 285°.
Reading a 360° protractor
A full-circle protractor removes the need to subtract. Put its center on the vertex and its 0° line on the first arm, then read around the circle in the direction the angle opens. If the scale has two rows, use the one that increases in that direction. It is especially useful for reflex angles, compass bearings and pie charts.
Tips for a precise reading
- Look straight down at the scale to avoid parallax.
- Use a sharp pencil; a 1 mm thick line on a 6-inch protractor is about half a degree wide.
- Extend short arms beyond the scale with a ruler.
- Use the biggest protractor you have. The marks are farther apart, so it is easier to split a degree.
Next: learn the whole routine in how to use a protractor, or see the types of angles.
Frequently asked questions
Why does a protractor have two sets of numbers?
So you can measure an angle that opens to the left or to the right without turning the protractor upside down. One row counts 0 → 180 from the right end, the other counts 0 → 180 from the left end. At any point the two numbers add up to 180°.
How do I read half degrees on a protractor?
Standard protractors only mark whole degrees, so you estimate: if the arm lies halfway between the 37° and 38° ticks, read 37.5°. For better precision use a larger protractor, a vernier bevel protractor, or the online protractor with 0.1° precision.
How do I read a 360° protractor?
Put the center on the vertex and 0° on the first arm. Then read around the circle in the direction the angle opens. The number where the second arm crosses is the angle, even if it is more than 180°.