PrintProtractor
Guide

How to use a protractor

A protractor measures the angle between two lines. The whole technique comes down to three things lined up correctly: the center hole on the corner of the angle, the baseline along one arm, and your eye reading straight down at the mark. This guide walks through measuring and drawing an angle, including the part that trips people up, which scale to read on a double-numbered protractor.

A protractor placed on a drawn angle, with the centre on the vertex and the baseline along one arm, and the second arm crossing the scale at 50 degrees.

The three things to line up

A protractor is a semicircle divided into 180 equal parts, each one degree. The centre of its baseline is the origin, the point you measure from.

"A protractor is a semicircular geometry tool divided into 180 equal parts, each measuring 1 degree." Its baseline meets a perpendicular line at the origin, the point you place on the corner of the angle.

Source: SplashLearn, Protractor: https://www.splashlearn.com/math-vocabulary/geometry/protractor

Measuring an angle comes down to lining up three things: the origin on the vertex, the baseline along one arm, and your eye reading straight down at the mark so you do not read it at a slant.

Measuring an angle

  1. Place the origin on the vertex. Put the centre hole or crosshair exactly on the corner where the two arms meet.
  2. Lay the baseline along one arm. Rotate the protractor until the zero line sits flush along one of the two arms.
  3. Find where the other arm crosses the scale. Follow the second arm out to the arc and read the number it points to.
  4. Read the scale that starts at zero on your first arm. If the first arm sat on the zero of the outer scale, read the outer numbers all the way round.

Drawing an angle

  1. Draw one arm and mark its end. This endpoint becomes the vertex.
  2. Set the origin on the endpoint, baseline on the arm. Just as when measuring.
  3. Mark your degree. Find the angle you want on the scale that reads zero along the arm, and make a small dot at it.
  4. Join the dot to the vertex. Use a straightedge to draw the second arm through the dot.

If you are reading off a printed protractor, it needs to be the right size, but for angle work the angles are correct at any scale. To draw at a precise distance, print one to scale with the protractor tool. The double scale, which trips up a lot of people, is covered in reading the inner and outer scale.

Related guides

Frequently asked questions

Which point of the protractor goes on the angle?

The centre point, called the origin, the small hole or crosshair at the middle of the baseline. Place it exactly on the vertex, the corner where the two arms of the angle meet.

How do I draw an angle of a given size?

Draw one arm, put the origin on its endpoint and the baseline along the arm, find your degree on the scale that starts at zero on that arm, mark it, then join the mark to the endpoint with a ruler.

Why does my reading look wrong?

Usually because the baseline was not flush with one arm, or you read the wrong one of the two scales. Make sure the zero you start from sits on one arm, then follow that same scale round to the other arm.