## What is a Protractor

A protractor is an instrument for measuring angles, typically in degrees. They come in semi-circle and full circle versions, though the semi-circle is the most common type. A semi-circle protractor measures 180° while a full circle ruler can measure 360°. Often protractors are clear so you can see your lines and shapes beneath the tool while measuring, and they have a series of tick marks along the outer edges for measuring angles.

## Using a Protractor to Measure an Angle

You can use a protractor to measure an angle by identifying the vertex, or center point, of the angle, placing the origin/center-point of the protractor over the vertex, lining up the bottom edge with one of the angle edges, and locating the measurement of the angle.

### Find the Vertex or Center Point of an Angle

The vertex of an angle is the point of intersection where two lines meet. Locate the two lines and see where they meet. If the two lines of the angle do not touch then use the straight portion of the protractor to extend the lines until they meet to find the vertex.

### Place the Protractor Origin Over the Vertex

Locate the origin near the straight edge of the protractor and in the center. There is usually a hole or circle marking the origin with vertical and horizontal cross-hairs to align the origin on the vertex perfectly. Align the horizontal edge of the origin with one of the edges of the angle so that the other edge of the angle extends to the measurements along the curved edge, as shown in the image above.

### Find the Angle in Degrees

#### Find the Acute Angle

An acute angle is the smaller angle where a line meets another, or technically any angle that is less than 90°. If a line were to meet another line forming two angles, the acute angle would be the smaller angle. With the origin of the protractor aligned over the vertex of the angle and the horizontal edge aligned with one of the lines, find the tick mark along the curve where the line meets. If the acute angle is on the left the tick mark will be on the outside, or outer-most edge, of the protractor. If the acute angle is on the right then the tick mark will be on the inside of the curve.

There are two rows of tick marks on a protractor to allow measuring the degrees of angle from either the left or right. The measurements should be incrementing in the direction you are measuring.

#### Find the Obtuse Angle

An obtuse angle is the larger angle where a line meets another, or technically any angle that is more than 90°. If a line were to meet another line forming two angles, the obtuse angle would be the larger angle. With the origin of the protractor aligned over the vertex of the angle and the horizontal edge aligned with one of the lines, find the tick mark along the curve where the line meets. If the obtuse angle is on the left the tick mark will be on the outside, or outer-most edge, of the protractor. If the obtuse angle is on the right then the tick mark will be on the inside of the curve.

### Useful Angle Tools

Since most protractors have measurements in degrees it is often necessary to use a formula to convert your measurement to radians, mils, or grads. Use our angle conversion tool to convert from degrees to radians, mils, or grads.

If you need a protractor you can download and print our printable protractor.