Protractors are a tool used in mathematics to measure angles in degrees. You may need a protractor to do your homework or design construction plans, so learning how to make one can be helpful. You can print a template or fold a square of paper so that you always have a protractor on hand.

## Steps

### Method 1 of 3: Print a protractor on paper

#### Step 1. Get heavy paper or transparent paper

Find a card stock or other heavy paper that will work for your printer. Heavy paper will make the protractor more durable. You can use transparent paper to make the protractor easier to use.

### Check your printer's instructions to make sure you can put clear paper on it before printing

#### Step 2. Download a protractor template

Download a protractor graphic for you to use. You can get a chart to download on the internet.

### You should choose an image that is large to achieve better quality. The clarity of the image will be determined by the size of the graphic file. You should be looking for an image that is at least 540X620

#### Step 3. Print the protractor chart

Use the printer to print the chart. Look for a preview of the image before printing to make sure it covers the entire conveyor.

### Change the image to the desired size for your protractor. In general, the straight edge of the protractor should be 3-6 inches (8-15 cm) long for best results

#### Step 4. Cut the protractor

Use scissors to cut the protractor shape out of the paper. Then cut out the center.

#### Step 5. Place the bottom edge of the cut on an angle line

Align the bottom edge of the protractor with one of the rays of the angle you want to measure. The angle measure is where the second ray of the angle crosses the curved section of the protractor.

### Method 2 of 3: Making a Pocket Protractor

#### Step 1. Cut a square out of a sheet of paper

Get an 8.5 x 11 inch (20 x 28 cm) sheet of paper to cut out a square.

- Use a ruler to measure 8.5 inches (20 cm) on the 11-inch (28 cm) side and make a mark at that point.
- Use the ruler to draw a straight line across the paper at the mark you made.
- Cut the paper along this line to end up with a 20 x 20 cm (8.5 x 8.5 inch) square piece of paper.

#### Step 2. Fold the paper in half

Fold the left side of the paper to the right side to create a crease in the middle. Then unfold the piece of paper.

- Align the edges of the paper precisely to make sure the crease is directly in the center of the paper.
- The precision of the angles will depend on the pleats being neat and exact.

#### Step 3. Fold the upper right corner to form a triangle

Take the upper right corner and fold it to a low point in the crease you made in the middle of the paper. Fold the corner down so that it meets the crease in the middle of the paper.

- The corner will be about 3/4 of the way down from the center crease you made when folding the paper in half.
- In this way, you will form a triangle on the paper with an angle of 30 °, another of 60 ° and another of 90 °.
- Fold the entire top edge of the paper down to create a new point at the top left of the paper.

#### Step 4. Fold the lower right corner up to form a second triangle

Grab the lower right corner towards the top edge of the first triangle. Fold until the right edge of the paper lines up with the folded edge of the first triangle.

### You will end up with a second triangle of 30 °, 60 °, and 90 °

#### Step 5. Fold the lower left corner up

Take the bottom left corner and fold it up until the left side of the paper meets the edge of the first triangle that was originally the top edge of the paper. Both edges should line up together.

### Insert the corner under the second 30 °, 60 °, and 90 ° triangle that you folded

#### Step 6. Label the angles on the protractor

The side of each different triangle forms a different angle that you must label. Lower the paper with the longest side pointing up.

- There are two angles at the top of the protractor. The left side has an angle of 15 ° and the right side one of 30 °.
- The left corner of your protractor has two angles. The angle at the top measures 45 ° and the angle at the bottom 30 °.
- The right corner of the protractor has an angle of 60 °.
- The angle made on the right side of the protractor (where a line passes through it) measures 90 °.
- The lower left corner contains a 45 ° angle to the right and a 30 ° angle to the left

#### Step 7. Use your pocket protractor

You can use it to measure angles in different shapes by matching the angles on the shape to those on the protractor.

- Find the degrees of the angles between the measurements of the protractor.
- You can divide the angles into smaller triangles by folding the triangles in half.

#### Step 8. Position the protractor over the angle you are trying to measure

Rotate the protractor to align the angles of the triangles on the paper with the angle you are measuring.

### Determine the angle you want to measure by matching it with the angles on the paper protractor

### Method 3 of 3: Draw a Protractor

#### Step 1. Use a ruler to draw a horizontal line

Draw a line on a sheet of paper that is 5 inches (12 cm) long. You can also use the bottom edge of the paper as the bottom edge of the protractor to skip this step.

### Make a mark in the exact center of the line 2.5 inches from the ends of the line

#### Step 2. Draw a semicircle with a compass

Use a compass to connect the edges of the line in a half-circle arc.

- Set the compass to create a circle with a diameter of 5 inches (12 cm).
- Draw a semicircle connecting the ends of your horizontal or centered line along the bottom edge of the paper.

#### Step 3. Fold a square piece of paper to create angle measurements

Take the square and fold it exactly in half and along each diagonal.

- A piece of origami paper is a good square to use.
- You can cut a perfect square by folding the top edge of a piece of printer paper to align with a side edge. Draw a line at the bottom where the paper crosses and cut the bottom section of the paper.
- Use the fully open square to draw a 90 ° angle on the protractor. Lay the bottom of the square along the bottom of the protractor. Align the edge of the square with the center of the line and trace along it.

#### Step 4. Mark the angles on the protractor

The square folded in half creates an angle of 45 °. Place the folded triangle along the bottom edge of the protractor and mark a line on the curved arc where the triangle crosses it. Label the line 45 °.

- Fold a triangle with an edge from the top left corner of the paper to the bottom center. This will create an angle of 60 °. Create the same crease from the right side to create a 120 ° angle. Mark these angles on the protractor. Make each crease on both sides of the triangle to create the complementary angles on both sides of the protractor.
- Fold a new triangle with the inside edge of the triangle extending from the upper left corner towards the center of the paper. The corner of the triangle will be located slightly to the right of the center of the paper and an imaginary line will extend from the corner to the bottom center of the paper. This will create an angle of 75 ° and 105 °.
- Flip the folded paper over and place the edge at the 90 degree angle on the protractor. At this point, the edge of the triangle should mark an angle of 15 and 165º.

#### Step 5. Cut the protractor

Use scissors to carefully cut the semicircle of the protractor.

### Cut a small "D" shape from the center of the protractor to see the angle lines you would like to measure

#### Step 6. Measure the angles

Place the bottom edge of the protractor along one edge of the angle you are measuring. Align the other leg of the angle with the curved arc of the protractor. Observe where the ray crosses the arc of the protractor to determine the angle you are measuring.

### Place the vertex of the angle where you marked the center of the bottom of the protractor

## Advice

- Wait until the ink dries completely on the transparent paper before cutting the conveyor. Ink can run if you try to cut the paper too soon.
- You must make the folds neat on the pocket protractor to get accurate angles.
- You can make larger angles on the pocket protractor by opening the pleats to double the angle.
- Tape the folded triangles in the center to make sure the pocket protractor holds its shape.