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Vernier calipers are cool!

And how to use them

March 6, 2024

mechanical

I wanted to share something cool I learned a few days ago with you all. So the back story is I lost my cheap battery powered caliper and I needed to get a new one since I’m doing doing a lot of cad for my robotics project. However I disliked having to buy batteries just to operate a measuring tool. I thought my only option was a dial caliper.

I didn’t want a dial since that’s just another mechanical point of failure. However there is actually another type of caliper I didn’t know about called a Vernier caliper. It uses a pretty neat trick.

My caliper
My caliper

So when I first saw this I was kind of confused. How could putting these extra scales (the top/bottom ones) result in finer measurement since they are about the same size as the main scale markings.

The way you use this caliper is a bit different. So if you put something inbetween the jaws, first you look at the primary scale (the bigger one) to get the first few digits (lets say we’re using mm).

Vernier Scale (credit Wikipedia)
Vernier Scale (credit Wikipedia)

If we look at the bottom-most scale, the 0 is between 3-4mm. Our goal is to estimate a few more digits if we can

So the way we get the extra digits is looking at how the bottom and top scales align. The point at which the lines perfectly line up with one another is where you take the measurement. So in this case we see that the lines match at 5.8 on the bottom scale, which is equivalent to 29 ticks (see in red).

To get our final answer we do

3mm + 29 ticks * (bottom scale size) = 3mm + 29*0.02 = 3.58mm

Conveniently the last two digits of precision are the same as the reading on the vernier scale (the smaller one). It still seems strange that we can be more precise than the precision of either scale.

The trick is that the spacing of the bottom scale is a fraction of the top scale. Lets say about 0.9 * top scale = bottom scale (not true to the picture)

If we look closely we can see that when both scales are lined up at 0, the other lines don’t quite match up

The scales don't line up
The scales don’t line up

So if we look at the 1 on the bottom scale, according to the scale on my caliper, the offset between the 1 and the closest line on top is 0.1mm since there are 5 ticks of each 0.02. For 2, the offset is 0.2mm, for 3 the offset is 0.3mm . And for 10 they completely align since 50 ticks * 0.02mm = 1mm

By comparing when the top and bottom scales line up you are essentially able to measure in increments of that offset between marks of the bottom and top scale.

Vernier constant

The Vernier constant is the smallest measurement you can make on this type of device i.e. a single tick on the vernier scale. On my device it takes 50 vernier ticks in order for it to correspond to 1mm on the main scale. So the vernier constant is 1mm/50 = 0.02mm precision.