How to Use a Protractor

A protractor measures angles in degrees. Most school protractors are half circles marked from 0° to 180°, with two sets of numbers running in opposite directions. Those two scales are the only tricky part, and once you know which one to read, measuring any angle takes seconds.

Parts of a protractor

• Center hole or crosshair: the point in the middle of the straight edge. It goes exactly on the corner of the angle, called the vertex.
• Baseline: the line that runs through the center point from 0° to 180°. On many protractors it sits a few millimeters above the plastic edge, so line up the printed line, not the edge.
• Outer and inner scales: two rows of numbers from 0 to 180. One starts on the left, the other on the right.

How to measure an angle

1. Put the center point on the vertex of the angle.
2. Turn the protractor until the baseline lies exactly along one side of the angle.
3. Find the 0 where that side meets the scale. It will be on the outer scale or the inner one.
4. Follow that same scale around to where the other side of the angle crosses it, and read the number.

In the picture above, the first side runs to the left through the outer scale’s 0, so the angle is read on the outer scale: 50°. The inner scale shows 130° at the same spot. That’s the angle on the other side of the line, not the one you’re measuring.

Quick sanity check: an angle narrower than a square corner is acute (less than 90°). One wider than a square corner is obtuse (between 90° and 180°). If your angle is clearly narrow but you read 130°, you used the wrong scale.

How to measure an angle larger than 180°

An angle between 180° and 360° is called a reflex angle. A half-circle protractor can’t read it directly:

1. Measure the smaller angle on the other side of the vertex, for example 110°.
2. Subtract it from 360°: 360 − 110 = 250°.

Our online protractor has a 360° mode that shows both angles at once. They always add up to 360°.

How to draw an angle

1. Draw a straight line with a ruler. This is the first side.
2. Mark a point on it for the vertex.
3. Put the protractor’s center on that point, with the baseline along your line.
4. Using the scale that starts at 0 on your line, make a small dot at the angle you want, for example 65°.
5. Remove the protractor and join the vertex to the dot with a ruler.

To draw a reflex angle, such as 300°, draw 360 − 300 = 60° instead. The reflex angle is the part on the outside.

Measuring angles without a paper protractor

• On screen: the online protractor works on any phone, tablet or computer. Hold an object against the screen, or add a photo and line the arms up with the angle in the picture. Angles don’t change when an image is enlarged or shrunk, so no calibration is needed.
• Printed: print a protractor at 100% scale, or use our printable ruler together with the right-triangle method below.
• With a ruler only: measure two sides of a right triangle and use trigonometry. The angle equals arctan(opposite ÷ adjacent). For example, a slope that rises 5 cm over 10 cm is arctan(0.5) ≈ 26.6°.

Common mistakes

• Center point off the vertex. Even 1–2 mm off can change the reading by several degrees on short lines.
• Using the plastic edge instead of the baseline. Line up the printed 0–180 line.
• Reading the wrong scale. Always start from the 0 on the first side.
• Sides too short. Extend them with a ruler until they reach past the scale.

Angles worth knowing

Angle	Name	Where you see it
90°	Right angle	Corner of a sheet of paper
45°	Half a right angle	Diagonal of a square
60°	—	Each corner of an equilateral triangle
180°	Straight angle	A straight line
360°	Full turn	A complete circle