Why use a vernier or a micrometer? A ruler can be read to about 0.5 mm. To measure the diameter of a wire, or the thickness of a coin, you need an instrument that can read to 0.1, 0.05 or 0.01 mm. Both of these use a clever trick to turn a tiny length into a big, easy-to-see reading. The smallest amount that an instrument can show is its least count (or resolution).

Vernier calliper. The sliding jaw carries a second scale, the vernier scale. For a calliper with a least count of 0.1 mm, 10 divisions of the vernier scale are the same length as 9 divisions of the main scale (9 mm), so one vernier division is 0.9 mm, and each is 0.1 mm shorter than a main scale division. Move the jaw by 0.1 mm and the next vernier line lines up with a main scale line. To read it:

1. Read the main scale at the zero line of the vernier scale (this gives the whole millimetres).
2. Find the vernier line that lines up exactly with any main scale line. Its number, times the least count, gives the fraction of a millimetre.
3. Add the two. The reading is (main scale reading) + (vernier line number) × (least count).

Micrometer screw gauge. The screw has a pitch of 0.5 mm, so one turn of the thimble moves the spindle 0.5 mm. The thimble has 50 divisions round it, so each division is 0.5/50 = 0.01 mm. The reading is the last mark on the sleeve that you can see (in steps of 0.5 mm: the marks above the line are whole millimetres and the marks below are halves) plus the number of the thimble division that lines up with the line along the sleeve, times 0.01 mm. Always close the micrometer using the ratchet at the end, so that you do not squash the object.

Zero error. When the jaws are closed the reading should be zero. If it is not, the instrument has a zero error. Measure it with the jaws closed. Then subtract it from every reading: corrected reading = measured reading − zero error. A zero error of +0.2 mm (the zero is beyond the line) means that every reading is 0.2 mm too big. A negative zero error means it is too small, so the correction adds to the reading.

What the picture leaves out. The instruments are drawn larger than life so that the lines can be seen. Click or drag on the scale to move the magnifier. The readings are always an exact multiple of the least count. When you take a real measurement, the last digit is an estimate, so you should write a reading with an uncertainty equal to the least count. If the lines on a vernier appear to line up at two places, the real reading is in between.

Things to try. (1) Read five vernier measurements, then check them. (2) Turn on the zero error, read the zero error from the closed jaws (the slider to 0), and use it to correct the reading. (3) Change to the 0.05 mm vernier. What changes? (4) For the micrometer, turn the thimble round once. How far does the spindle move?