How to Use a Protractor
Put the vertex of the angle on the protractor's centre mark, not on its edge, and lay one arm along the zero line. Then read the scale that starts at zero on that arm — the two scales run in opposite directions and reading the wrong one gives you 180 minus your angle, which is why a 60° angle so often comes out as 120°.
A protractor has two number scales running in opposite directions, and picking the wrong one is the single most common mistake with the tool. The fix is to decide first whether the angle is acute or obtuse, then read the scale that agrees with you.
Line up the vertex first
The small cross-hair or hole at the centre of the flat edge goes exactly on the point where the two lines meet. The flat edge then runs along one of the arms. If the arm is too short to reach the edge of the protractor, extend it with a pencil line — measuring off a short arm is where most of the error comes from.
Pick the scale before you read it
Both scales are correct; they just start from opposite ends. Decide by eye whether the angle is less than a right angle or more, then read the number that matches. An angle that clearly looks acute cannot be 130°.
The two readings always sum to 180. If you get 50 on one scale and 130 on the other, you have read both correctly and only need to pick.
Angles over 180 degrees
A standard protractor stops at 180°. For a reflex angle, measure the smaller angle on the other side and subtract from 360. A 210° angle reads as 150° from the other side.
Degrees, grade and pitch are the same thing
Builders quote slope as pitch — rise per 12 of run. Drainage code uses grade, a percentage. Saws are set in degrees. A 4/12 roof is an 18.4° angle and a 33.3% grade; all three describe one slope.
A printed protractor works for this, but a pitch gauge held against the rafter is faster and does not need the vertex to be reachable.
Questions people actually ask
- Which scale do I read, inner or outer?
- Whichever agrees with what you can see. The two always add to 180, so if the angle looks smaller than a right angle, take the reading under 90.
- How do I measure an angle with no clear vertex?
- Extend both arms with a straightedge until they cross, then measure at the intersection. This is the normal approach for a roof pitch measured from a gable end.
- How accurate is a printed protractor?
- Within about half a degree if it is printed at 100% and checked against the reference bar. That is finer than most saw scales read.
Sources: Wolfram MathWorld — angle measure, NIST Office of Weights and Measures