# How to use a protractor if you can't see what you are measuring?

I have this protractor:

It seems to be the same or similar as this one: Robinson 5001# Stainless Steel Protractor RBS-R-5001 but there are no instructions there.

The main problem with this protractor is that the 'origin' swivel point can't be accurately placed over the object you are trying to measure because you can't see where it is. For instance if you put it over a paper image of a triangle to measure an interior angle you can line up the tip of the protractor (small detent) but not the swivel point.

Also I don't see how you could use this e.g. to measure the interior angle of a real object as you would with a bevel gauge. So it does seem intended to be used for flat measurements, I just can't see how.

• Could you explain that two or three different ways, please? If the 'origin' swivel point can't be accurately placed, what else could be accurate? If you're really Asking how the protractor could be accurately placed isn't that a very different Question? Commented Dec 10, 2020 at 22:56

The angle between the ruler part and the the semicircular part is the same as the angle indicated on the scale. This is because the centreline of the ruler is parallel to its edge.

In more detail:

Image from Wikimedia Commons user Krishnavedala

Consider line a to be the top edge of the ruler in the picture and line b the centreline. Line t, the transversal, is the base of the semicircle. The top right θ where a and t meet is the angle you want to measure. The bottom left θ is the angle the pointer makes with the semicircle.

This is a useful protractor for setting an angle or measuring a physical object with some thickness. For work purely on paper I'd prefer the clear plastic sort, marking in pencil and then using a steel rule for cutting if necessary.

Say you want to measure the interior angle of the parallelogram shown in freehand blue in this picture (imagine it drawn on paper under the ruler).

You align the protractor as shown, so the edges highlighted in thin red run along the lines you're interested in. Then the other angle in red is what you read off. This is a copy of the first red angle, rotated and enlarged (hence thicker), but not distorted. You can see that this runs through the pivot and point to the pointer, aligned with its groove. NB: Somehow I've actually placed the lower red angle in slightly the wrong place, aligned with the base of the (slightly more than) semicircular part instead of the zero line.

• So, you think its more for measuring an exterior angle than an interior one? (even on a flat surface, like paper) Commented Dec 8, 2020 at 13:31
• On paper you can easily measure an interior angle, though you're effectively measuring the corresponding exterior angle and subtracting from 180°. I'm marling up your photo now Commented Dec 8, 2020 at 13:34

To place this protractor or any measuring tool at a difficult to see point use a stylus such as a pencil or an awl or the metal tip of a compass. Place the point of the stylus on the given point and slide the protractor's two beams against it so that it rests at their intersection.

If the stylus is too thick you may need to angle it away from the protractor beam edges so that the side touching the beam aligns exactly with the point.

As Chris H explains, the measured angle is the same even if the center point is offset from the origin since the available edge and the baseline of the tool's center point are parallel.

• I think you mean instead of center mark (which is under the knob) the inside corner of the protractor? That does sound like a good method to align it. Commented Dec 9, 2020 at 20:46
• I see, adjusted answer accordingly. Commented Dec 9, 2020 at 20:51