November 3, 2026 · Indumor
In this chapter
Half past seven, the shop still cold. The apprentice brings a bushing fresh off the lathe and says it measures 24.95; the foreman puts a micrometer on it and gets 24.98. Both read correctly. What changed was the instrument, and the force the apprentice used to close the jaws. This chapter is here so that argument lasts ten seconds.
A caliper carries two scales. The main scale, on the beam, is in millimeters. The vernier, on the slider, has divisions slightly smaller than the beam's: on the 20-division vernier spread over 39 mm each one is 1.95 mm, five hundredths short of two millimeters. That is why only one vernier line ever lines up with a beam line, and which one it is tells you how many hundredths to add.
a: least count. d: smallest division of the beam (1 mm, 1/16 in, 1°). n: number of vernier divisions. k: number of the vernier line that coincides. On a micrometer, a = screw pitch / thimble divisions = 0.5 / 50 = 0.01 mm.
Reading takes two steps: the last whole millimeter the vernier zero has passed, plus the number of the coinciding line times the least count. Only one line coincides; its neighbours are offset one way and the other. In figure 1 the zero is past 23 and line 13 coincides: 23 + 13 × 0.05 = 23.65 mm.
| Vernier | Beam division | Vernier divisions | Vernier length | Least count |
|---|---|---|---|---|
| Tenths of a millimeter | 1 mm | 10 | 9 mm | 0.1 mm |
| 0.05, short | 1 mm | 20 | 19 mm | 0.05 mm |
| 0.05, long (figure 1) | 1 mm | 20 | 39 mm | 0.05 mm |
| 0.02 | 1 mm | 50 | 49 mm | 0.02 mm |
| Fractional inch (figure 3) | 1/16″ | 8 | 7/16″ | 1/128″ (0.198 mm) |
| Decimal inch | 0.025″ | 25 | 0.6″ | 0.001″ (0.0254 mm) |
| Decimal inch, long | 0.025″ | 25 | 1.225″ | 0.001″ (0.0254 mm) |
| Universal bevel protractor | 1° | 12 | 23° | 5′ |
| Instrument | Beam shows | Coincides | Sum | Reading |
|---|---|---|---|---|
| Caliper, 0.1 mm vernier | 12 mm | 7th | 12 + 7 × 0.1 | 12.7 mm |
| Caliper, 0.05 mm vernier (figure 1) | 23 mm | 13th | 23 + 13 × 0.05 | 23.65 mm |
| Caliper, 0.02 mm vernier | 41 mm | 36th | 41 + 36 × 0.02 | 41.72 mm |
| 0.01 mm micrometer (figure 2) | 7 mm, no half-mm line | 36 on the thimble | 7 + 36 × 0.01 | 7.36 mm |
| 0.01 mm micrometer, half-mm line showing | 12.5 mm | 18 on the thimble | 12.5 + 18 × 0.01 | 12.68 mm |
| Inch caliper, 1/128 vernier (figure 3) | 1 5/16″ (21/16) | 3rd | 1 5/16 + 3/128 | 1 43/128″ = 33.93 mm |
| Inch caliper, 0.001″ vernier | 1.350″ | 17th | 1.350 + 17 × 0.001 | 1.367″ = 34.72 mm |
The 0.02 mm vernier is harder on the eyes because the neighbouring lines are off by only two hundredths. Inch calipers come with two verniers: the fractional one, 8 divisions over 7/16 in, resolves 1/128 in and is added up in sixteenths and 128ths; the decimal one, 25 divisions against a beam graduated in 0.025 in, resolves one thou. To convert to millimeters use the inch table or chapter 1.
A micrometer measures with a screw of 0.5 mm pitch: one turn of the thimble moves the spindle half a millimeter and, since the thimble has 50 divisions, each one is a hundredth. The sleeve shows whole millimeters above the reference line and half millimeters below it. The reading adds the whole millimeters uncovered, the half millimeter if it shows, and the thimble division that lines up with the line.
The classic mistake is missing the half millimeter: if the thimble reads 36 and the lower line is already out, the part measures 7.86, not 7.36. When the line sits right at the edge the thimble settles it: near 0 it just came out; near 50 it has not yet. The sleeve vernier, ten lines spanning nine thimble divisions, adds the micron; for it to mean anything you need the ratchet stop and the part at the same temperature as the instrument, and DIN 863 allows a 0-25 mm micrometer up to 4 µm of error anyway. The inch micrometer has a 40 tpi screw: one turn is 0.025 in, the thimble has 25 divisions of 0.001 in and the vernier adds the tenth, 0.0001 in. The zero is checked with the spindle closed or against the setting standard from the case.
The caliper and the micrometer cover most measurements, not all of them; the table collects the rest of the bench with least count, range and standard. Two notes. Go/no-go gauges do not measure, they pass or fail (the go side enters, the no-go side does not), which is how a hundred identical parts get checked without reading anything. The dial indicator does not measure a dimension either: it compares against a reference, which is how work gets centered in the lathe or a shaft checked for runout.
| Instrument and standard | Least count | Typical range | What it is for |
|---|---|---|---|
| Vernier caliper ISO 13385-1, DIN 862 | 0.1 / 0.05 / 0.02 mm | 150, 200, 300 mm | Outside, inside, depth and steps |
| Dial caliper ISO 13385-1 | 0.02 mm (también 0.01) | 150 to 300 mm | Same jobs, quicker to read |
| Digital caliper ISO 13385-1, DIN 862 | Resolution 0.01 mm; allowed error ±0.02 to ±0.03 | 150 to 300 mm | Same jobs; inch/mm at a button |
| Vernier depth gauge DIN 862 | 0.05 / 0.02 mm | 150 to 300 mm | Hole depth, steps and grooves |
| Height gauge DIN 862 | 0.02 / 0.01 mm | 300 to 600 mm | Scribing and measuring on the surface plate |
| Outside micrometer ISO 3611, DIN 863 | 0.01 mm; 0.001 with vernier | 0-25 to 275-300, in 25 mm steps | Diameters and thicknesses with tight tolerance |
| Three-point bore micrometer DIN 863 | 0.005 / 0.001 mm | 6 to 300 mm | True diameter and out-of-roundness of bores |
| Depth micrometer DIN 863 | 0.01 mm | 0-25 to 0-300 with rods | Depth of seats and grooves |
| Dial indicator ISO 463, DIN 878 | 0.01 mm (10 mm travel); 0.001 mm (1 mm travel) | Travel 1 to 10 mm | Centering, alignment, runout and flatness |
| Dial test indicator (lever) DIN 2270 | 0.01 / 0.002 mm | Travel 0.8 mm | Centering on lathe and mill, probing grooves |
| Universal bevel protractor | 5′ | 0 to 360° | Part angles and tool angles |
| Go/no-go gauges (plug, snap, ring) ISO 1938-1 | They do not measure: pass or fail | Per dimension | Fast checking of holes, shafts and threads in series |
| Feeler gauges | Blades from 0.05 to 1 mm | 0.05 to 1 mm | Gaps between parts, valve clearance |
| Thread pitch gauges | Pitch | 0.25 to 6 mm; 4 to 62 tpi | Identifying the pitch of a thread |
| Radius gauges | Radius | 1 to 7 mm and 7.5 to 15 mm | Radii and fillets |
| Sine bar | With gauge blocks: 1′ or better | 5 in, 100 or 200 mm between rolls | Exact angles for grinding and inspection |
| Gauge blocks ISO 3650 | Grade 0: ±0.12 µm; 1: ±0.20; 2: ±0.45 (up to 10 mm) | 0.5 to 100 mm, in sets of 32 to 112 | Calibrating micrometers, setting the sine bar |
The universal bevel protractor reads like a caliper: a 12-division vernier over 23°, least count 1° divided by 12, five minutes. A sine bar sits on gauge blocks stacked to h = L · sin α (L: distance between its rolls) and tilts the part to the exact angle. Gauge blocks are the reference for everything else: a grade 1 or 2 set checks the micrometer; grade 0 is kept for calibration.
The practical rule is the rule of ten: the least count of the instrument should be at most one tenth of the tolerance. A shaft with 0.2 mm of tolerance is measured with a 0.02 caliper; one with 0.02 mm calls for a 0.001 micrometer. Never one to one: a 0.05 caliper does not check a 0.05 tolerance. How many microns an H7 or a g6 is comes in chapter 3. And watch digital calipers: they display hundredths, but DIN 862, the catalogs' reference, allows them 0.02 to 0.03 mm of error. Resolution is what the display shows; accuracy is what the instrument guarantees.
Measuring force is the first: close the caliper until the jaws touch the part, without squeezing, because squeezing reads up to five hundredths under; the micrometer has a ratchet for this. The second is parallax: read the vernier straight on. The third is play in the slider, found by closing it against the light. The fourth is position: the part goes as deep into the jaws as possible and square to the slider. The fifth is temperature. And before all of that, the zero: clean faces, instrument closed, and it must read zero.
Care is the usual list that almost nobody follows: clean, with a drop of light oil, kept in its case rather than on the lathe bed among the chips, never used to scribe or as a divider, away from magnetic bases, and checked against gauge blocks once a year.
Every dimension on a drawing holds at 20 °C: ISO 1 fixes that reference temperature. Steel grows 11.5 microns per meter per degree, which sounds small until it is set against a tight tolerance: a 300 mm shaft that comes off the lathe at 45 °C measures almost nine hundredths more than it will cold. A shop floor is not air-conditioned, but the part can be left to cool, measured away from the sun and the welding bay, with a micrometer at room temperature and, when needed, corrected with the formula.
Δl: growth or shrinkage (mm). l: measured length or diameter (mm). α: coefficient of linear expansion (1/°C; steel 11.5 · 10⁻⁶). Δt: part temperature minus 20 °C.
| Material | α 10⁻⁶/°C | 100 mm µm | 300 mm µm | 1000 mm µm |
|---|---|---|---|---|
| Carbon and low-alloy steel | 11.5 | 11.5 | 34.5 | 115 |
| Austenitic stainless steel (304, 316) | 16.0 | 16.0 | 48.0 | 160 |
| Gray cast iron | 10.5 | 10.5 | 31.5 | 105 |
| Aluminum and its alloys | 23.0 | 23.0 | 69.0 | 230 |
| Brass | 19.0 | 19.0 | 57.0 | 190 |
| Bronze | 18.0 | 18.0 | 54.0 | 180 |
| Copper | 16.5 | 16.5 | 49.5 | 165 |
| Titanium | 8.6 | 8.6 | 25.8 | 86 |
| Invar (Fe-Ni 36 %) | 1.2 | 1.2 | 3.6 | 12 |
The coefficients hold between 20 and 100 °C and vary with the alloy: for a fine calculation use the one from the material data sheet.
Worked example · a hot shaft that looked good
A Ø80 steel shaft comes off the lathe and the micrometer reads 79.98 mm; the drawing asks for 79.97 to 79.99. Looks fine. But the contact thermometer says the part is at 45 °C and the micrometer at 20 °C.
The sum works backwards too: if the part has to measure 79.98 cold, at 45 °C it must read 80.003.
Δl = l · α · Δt with the coefficients from the table. Use it to turn a measurement taken hot into what the part will measure cold.
Count the vernier divisions and pick how the beam is graduated. Rule of ten: that value should be ten times smaller than the tolerance you are going to check.
One last piece of advice: a dimension that cannot be reworked gets measured twice, the second time with a different instrument.
Note the last whole millimeter the vernier zero has passed and find the only vernier line that coincides with a beam line. Reading = millimeters + number of that line × 0.05. If the zero is past 23 and line 13 coincides, the reading is 23.65 mm.
Add the whole millimeters uncovered on the sleeve, the half millimeter if the lower line is already out, and the thimble division that lines up with the reference line, worth 0.01 mm. With 7 mm, no half line and the thimble on 36, the reading is 7.36 mm.
Because ISO 1 sets that reference temperature for every dimension on a drawing. Steel grows 11.5 microns per meter per degree: a 300 mm shaft measured at 45 °C reads almost 0.09 mm more than it will cold.
Sources: ISO 13385-1 (calipers); ISO 3611 (outside micrometers); ISO 1 (standard reference temperature, 20 °C); ISO 3650 (gauge blocks); ISO 463 (dial indicators); ISO 1938-1 (plain limit gauges); DIN 862; DIN 863; DIN 2270; ASME B89.1.13 (micrometers); ASME B89.1.14 (calipers). Expansion coefficients: typical values from steel and alloy data sheets.
How many microns an H7 or a g6 is, and which instrument it takes to check them.
Read →We machine it in our shop in Córdoba, Argentina, and ship it measured, with its inspection sheet.
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