Introduction: Protractor - Measuring Angles

Now we're going to make a protractor! A Protractor is one of the most basic, but essential, tools for making measurements. It is, then, surprising that the modern protractor is barely over 200 years old.

A protractor measures angles from a point, along two radiuses, one aligned with the bottom, and the next aligned with a mark made along the circumference of the protractor.

Today, we're going to explore the protractor, and through building it, gain a deeper understanding about using it.


  1. Continue to the next step

Step 1: Set Up Work Environment

We will be making extensive use of the Ruler Helper, perhaps in ways you have not done before. Therefore, it is important that we begin with it in the right place.

It is common with most tools, on a computer or in the real world, to set up the work environment, first, so everything you'll need will be at your disposal.


  1. Drag the Ruler Helper so that its Origin is at the center of the Workplane. Make sure to align the axes of the ruler tool to a major (thicker) grid line. Grid lines are 1mm apart and major grid lines happen every 10mm. Aligning this ruler helper to the major grid lines helps you make movement decisions faster.
  2. Today, we'll be using the Ruler Helper in "Use midpoint" mode. We will not be able to set the mode until we have placed an object on the workplane. Drag out our first piece, a cylinder. We don't need to worry about being precise in placement, the ruler helper will allow us to have fine grained control over the placement of objects.
  3. Select our new cylinder. You'll notice a small triangle or arrow below the object, centered on its X axis. If you hover over the triangle, you'll see the text 'Use midpoint' appear. If you click this, it will change the mode. The text will then change to 'Use corner' which will let you know you are in midpoint mode.
  4. You'll now notice that the Ruler Helper measures from the origin to the center of the object. If you click on the measurements along the X and Y axes and set them to Zero, your object will move to be perfectly centered on the origin. Since we are designing a protractor, this will be the point from which all measurements, while using the protractor, will radiate.
  5. Continue to the next step.

Step 2: Making the Arc

The basic form of a protractor is an arc with demarcations along its edge. In this step, we'll make that arc.


  1. Resize your existing cylinder to be 150mm in diameter and 3mm along the Z axis. Then, make sure its center is 1.5mm above the workplane (1.5mm on the Z axis.) Remember, we are in midpoint mode, so the distance measure along the Z axis will be to the middle of the object, not the bottom.
  2. Drag another cylinder to the center of the other. You can't see the grid lines, so just eyeball it, and then correct the position using the Ruler Helper.
  3. Continue to the next step.

Step 3: Bevel the Edge (1 of 2)

We'll want the edge of our protractor to be thin while keeping the rest of the protractor ridged. So what we'll do is keep the body 3mm but taper the edge almost to a point. This type of feature is referred to as a beveled edge.

Think of a bevel as cutting an sharp edge off to make two edges which are half as sharp.


  1. Set the second cylinder to be 160mm in diameter and 20mm tall, then move its center to 11mm above the Workplane.
  2. For the next few steps, I have set the cylinder to a hole just so we can see through it.
  3. Drag out a cone, but keep it outside of the cylinder so the cylinder won't be in the way when we resize the cone.
  4. Continue to the next step.

Step 4: Bevel the Edge (2 of 2)

Continued from previous step


  1. Make the cone 150mm in diameter and 20mm tall. Move its center to 11mm off of the Workplane and center the cone to the origin.
  2. Turn the cone in to a hole, and turn the cylinder in to a solid (color).
  3. What we are now going to do is remove the cone from the larger cylinder. Select all the objects, then unselect the bottom cylinder, and press group.
  4. Turn this object in to a hole. You should now have a hole in the shape of a negative of a cone.
  5. Group this shape and our first cylinder. This will make a bevel on our protractor.
  6. Continue to the next step.

Step 5: Make the Straight Edge

Now we're going to cut the protractor in half to create the straight edge.


  1. Drag a box to the workplace and make it larger than half off the cylinder. I made mine 160mm by 80mm.
  2. We will then center it on the X axis, but we will align the edge to the Y axis. To do this, take the box's Y dimension and divide it in half. Use this number to move the box below the Y axis by making this value negative. In my case, the center of the box will be at -40mm on the Y axis.
  3. Make this object a hole and then group it with the cylinder.
  4. Continue to the next step.

Step 6: Make the Focal Point

The focal point of a protractor is where the two lines, which define an angle, meet. We need to make a space for the point to be visible so we are able to view the point from which the two lines radiate.


  1. Create a cylinder that is 16mm in diameter and 3mm tall. Center it on the origin, and move the center of the cylinder 1.5mm above the workplane.
  2. Group this object with the semi-circle.
  3. Drag out a cone to the center of the ruler and rotate it 180° around the Y axis so that the point of the cone points in the negative direction along the Z axis.
  4. Make the cone 7mm tall and move it so it's center is 2.5mm above the workplane.
  5. Turn the cone in to a hole and group everything.
  6. Continue to the next step.

Step 7: Cut the Window (1 of 2)

We'll need a viewing window through which we read the lines when we are measuring.

We have an opportunity, now, to customize your protractor. For instance, how thick do we want the straightedge rule and the protractor rule to be? I chose 15mm and 20mm, respectively, but you may make these features smaller, leaving more room for the window. I'll show you how I came to my measurements so, if you like, you can calculate your own.


  1. Drag out a new cylinder and center it to the origin along the X and Y axes. My protractor is 150mm in diameter, so to make a 20mm wide rule, I need to subtract 20mm from 150mm, twice (150-40=110mm). I made my cylinder 110mm in diameter.
  2. Drag out a new box and center it to the origin along the X axis. Make it larger than half of the new cylinder. The critical dimension is the Y axes. I made my box's Y axis dimension 74mm.
  3. To make a 15mm wide straightedge rule, divide the Y axis dimension of the box in half (74/2=37mm) and then subtract our desired dimension from this (37-15=22m). Move the center of this box to -22mm on the Y axis.
  4. Continue to the next step.

Step 8: Cut the Window (2 of 2)

Continued from previous step


  1. Make the box a hole and group the new cylinder and the box together.
  2. Turn this new shape in to a hole and group it with the rest of the protractor.
  3. Continue to the next step.

Step 9: Create Demarcations (1 of 2)

We now have a pristine protractor shape, but it isn't very useful without degree demarcations. For ease of reading, we will make three styles of demarcation, one length for intervals of ten, a shorter length for measures ending in five, and the shortest length for all other measures.

I am making my demarcations 10mm long, 8mm long, and 7mm long, respectively. If you'd like to customize yours, refer back to step 8!


  1. Drag out a box and make it 150mm along the X axis and 0.5mm along the Y axis.
  2. Drag out another box and make it 130mm along the X axis. Make it 3mm tall (along the Z axis) and move its center so it is 1.5mm off of the workplane. Turn it in to a hole.
  3. Use the Align tool to center these objects to each other on the X and Y axes, and so they share lower Z limits.
  4. Duplicate these shapes twice more so you have three sets total.
  5. We will leave one of these pairs of objects alone, and we'll use that for the degree intervals of 10.
  6. Then, we will change one of the copies, for the intervals ending in 5, so that the hole is 134mm long.
  7. The last, for all other intervals, set the hole to be 136mm long.
  8. Then, group these pairs of objects. Do not group them all together, just each hole with its corresponding box so we have three separate objects.
  9. Continue to the next step.

Step 10: Create Demarcations (2 of 2)

Now we will rotate these new objects so that we can assemble them to define a single interval of demarcations from 1 to 10.


  1. Leave the object for measures at intervals of 10 degrees alone.
  2. Take the object we made for the measures ending in 5 and rotate that shape about the Z axis in the positive (clockwise) direction by 5°.
  3. Take the object we made for all other measures and rotate it 1°, then duplicate it, then rotate the duplicate one degree, then duplicate it two more times.
  4. Duplicate these 4 objects and rotate them 5°. There should be a gap after the fourth mark.
  5. Select all of these objects and align them to each other so that they all share the same center.
  6. Continue to the next step.

Step 11: Inspect Demarcations

Now that we have one sequence of demarcations, it is easy to replicate them for every 10 degrees.


  1. Look at this new group of objects from below the workplane. You should see something like what is above. Eight short marks, one medium mark, and one long mark.
  2. Group these objects.
  3. Continue to the next step.

Step 12: Place First Demarcations

We're going to place and inspect the first group of demarcations.


  1. Move this group so that its center is located at the origin, and above the workplane 11mm (11mm positive on the Z axis.)
  2. If you look at the straight edge of the protractor, you should see that the longest of the demarcations is half on and half off the edge. This is EXACTLY where we want the mark.
  3. Continue to the next step.

Step 13: Place the Remaining Demarcations

We are going to duplicate and rotate the demarcations until we make a complete circle.


  1. Select the first group of demarcations and duplicate them.
  2. Rotate the duplicate demarcations by 10°.
  3. Repeat this process until you have completed the arc.
  4. Group all of the shapes which represent the demarcations and put this group in to hole mode.
  5. Finally, combine this group of shapes and the blank protractor in to one shape.
  6. YOU WILL NOTICE that we have 180° of demarcations that will be cutting in to nothing.Why is this? Tinkercad allows us to rotate objects around their center. The challenge is, sometimes we want to rotate an object around a different point. So what we have done is extended the size of the object so that the point we wish to rotate the object around IS the center of the object.This will become more clear when we place our lettering.
  7. Continue to the next step.

Step 14: Check Your Work

Lets take a moment to check if our demarcations are right.

If you notice, the protractor is already doing its job. The focal point is on the origin, the straight edge is in line with the X axis, the measures for 0° and 180° are along the X axis. The measure for 90° is along the Y axis.

If this is true for your protractor, good job!


  1. Continue to the next step.

Step 15: Placing First Number

We are going to label this protractors increments of 10, starting with the 90 degree demarcation up at the top.

Placing the text, formatting the text, and scaling the text are all arbitrary. What is key is that the text fits, is large enough to print, but is not so large that the text will crowd the neighboring text.


  1. Use the Text shape generator to create the first label, at the center most demarcation, and enter the text "90".
  2. Decide now if you want raised text, recessed text, or text that goes all the way through.
  3. If you want the text to cut all the way through your protractor, you will need to choose a stencil font, which 4. means a font that has bridges to hold the centers of lettering to the rest of the part. In the Text tool, Majorsnafu is the only stencil font in Tinkercad.
  4. Position your font, along the Z axis, how you want it. I want recessed text, so I put the bottom of the text 1mm below the top surface of the protractor.
  5. Continue to the next step.

Step 16: Making the Text Easy to Rotate About the Z Axis

Now we need to rotate the text along the arc. This would be painstaking, but we just learned a trick to make this easy. Again, we are going to make sure that the text rotates, easily, around the origin.


  1. Drag a block to the origin of the Ruler Helper
  2. Resize it to so that it's length along the Y axis is 150mm.
  3. Position the block so that it is completely beneath the workplane (the top of the block is at a negative Y Value.)
  4. Make sure the object is centered (that the center of the object has an X and Y positional value of 0.)
  5. This new object is our Rotational Helper
  6. Group your lettering and your Rotational Helper together.
  7. Continue to the next step.

Step 17: Duplicate and Place the Remaining Text.

Like with the demarcations, we are going to rotate the lettering around the origin, but unlike the demarcations, the lettering is completely outside of the origin. Therefore, to make the rotation easy, we added the lettering to a group which DOES have a center which coincides with the origin, at least on the X and Y axis.


  1. Duplicate the group with the lettering
  2. Rotate the lettering 10°
  3. Repeat in both directions in 10° increments
  4. Continue to the next step.

Step 18: Delete the Rotational Aides.

Our Rotational Helper has done its job. It is now time to remove it.


  1. Ungroup the lettering groups.
  2. Delete all of the Rotational Helpers.
  3. Continue to the next step.

Step 19: Edit the Lettering

Now, we just need to edit the lettering to match the angular measure.


  1. Change the lettering to match your desired numbering scheme.
  2. If you want to make stencils or recessed text, turn the text objects in to holes.
  3. Group the lettering and the protractor.
  4. Continue to the next step.

Step 20: Print Your Protractor

This object, which is nearly completely flat, will not have a problem printing. Depending on the size of your lettering, the lettering may not be clear. You may have to scale the object or your lettering to be larger so that the lettering prints clearly.


  1. From the Design menu, click 'Download for 3D Printing'.
  2. Click the button labeled 'STL'.
  3. When your browser has completed downloading, load the file in to your 3D printer software.
  4. This object doesn't require any special settings.
  5. Print!