# How Vernier Scale Works

## An Intuitive Understanding

Before the days of digital calipers with LCD display, one learns how to read the Vernier scale on a metal caliper directly. There are still tutorials teaching how to read such a metal caliper correctly.

Once you learn how to use the aligned number on the Vernier scale to read out sub-millimeter, have you wondered why does it work like that?

To gain an intuitive understanding, let’s start with the zero position of a caliper (with sliding Vernier scale in yellow):

If you look at the 50th big division mark (marked as 0 on the right, after the number 9) on the yellow Vernier scale, it matches the 49mm mark on the main scale. In other words, it’s 1mm short of 50mm mark. Because this Vernier scale has 50 (5 x 10) total division marks, this 1mm shortage is evenly distributed among them, i.e. each Vernier division is 0.02mm (1/50) shorter than the 1mm it represents (50mm mapped into 50 divisions).

Thus, instead of marking 0, 5, 10, …, 50 mm on the Vernier scale, which would be just like the main scale, the marking 0, 1, 2, 3 indicates the total shortage in mm. For example, 5 mark on the Vernier scale occupies 25 divisions, since each division is 0.02mm shorter, that 5 indicates 0.5 mm shortage.

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memento of electronics and fun exploration for my future self