Measuring and tolerances
With a tape measure, a ruler or a caliper you measure to the millimetre or even to 0.1 mm. A tolerance says how much a size may vary.
Why
Why does a battery from any shop always fit in your remote control?
No part comes out of a machine at exactly the right size. One is a fraction thicker, another a fraction thinner. Yet batteries, screws and bike tyres from different factories fit together just fine.
That is because the designer writes down not only a size, but also how much it may vary. As long as every part stays within those limits, everything fits. To check that, you have to be able to measure precisely.
See it
Pick a part: a shaft of 20 ± 0.1 mm, a small board of 120 ± 1 mm or a bush of 8.0 ± 0.05 mm. Slide the measured size back and forth and see whether the part is approved or rejected.
- Reading
- 20 mm + 1 · 0.1 mm = 20.1 mm
- Allowed
- 19.9 … 20.1 mm
Description of the picture
A caliper around the chosen part. You see the main scale in millimetres and the vernier that reads to 0.1 mm or 0.05 mm. A band below shows the smallest and the largest allowed size. If the measured size is inside the band it says approved, otherwise rejected.
Get it
Every measuring tool has its job. With a tape measure you measure long lengths, such as a room or a board, to the millimetre. With a ruler you measure short lengths to the millimetre. With a caliper you measure small parts to 0.1 mm or even 0.05 mm: the outside size with the big jaws, an inside size with the small jaws at the top and a depth with the rod at the back. Do not forget the units: 1 cm is 10 mm, 1 m is 100 cm or 1000 mm. On technical drawings everything is in millimetres.
You read a caliper in two steps. First read the whole millimetres on the main scale, just to the left of the zero of the vernier. Then look for the vernier line that lines up exactly with a line on the main scale. If that is line 4, you add 0.4 mm. If the zero is just past 23 mm, you read 23.4 mm.
A size like 20 ± 0.1 mm has two parts. The nominal size is 20 mm: the size the designer means. The tolerance is 0.1 mm: that is how much bigger or smaller the part may be. So the smallest allowed size is 19.9 mm and the largest is 20.1 mm.
When you check, you compare the measured size with those limits. If it lies between them, the limits included, the part is approved. If it lies outside, it is rejected. A shaft that is too thick can sometimes still be sanded down. A shaft that is too thin usually cannot be saved.
The smallest allowed size is the nominal size minus the tolerance, the largest is the nominal size plus the tolerance. In between: approved. Caliper: whole millimetres on the main scale plus the matching vernier line times 0.1 mm.
Worked example
A shaft must be 20 ± 0.1 mm thick. You measure 20.2 mm with the caliper. Is the shaft approved or rejected?
Work out the smallest allowed size.
20−
0.1= 19.9 Work out the largest allowed size.
20+
0.1= 20.1 20.2 mm is bigger than 20.1 mm, so the shaft is outside the limits.
- Answer
The shaft is rejected: it is 0.1 mm thicker than the largest size allowed.
Do it
Pick a level. You get a new exercise every time, checked straight away.
Make it
Become a quality inspector30 minutes
What you need
- ten objects of the same kind, such as wooden clothes pegs or new pencils
- a ruler and, if you have one, a caliper
- a sheet of paper and a pen
- someone who wants to measure with you
How to do it
- Choose which size you will check, for example the length of a clothes peg.
- Measure one piece very carefully. That size becomes your nominal size.
- Agree on a tolerance: ± 1 mm if you measure with a ruler, ± 0.2 mm with a caliper.
- Work out the smallest and the largest allowed size and write them at the top of your sheet.
- Measure all ten pieces and write down each size with its unit.
- Write approved or rejected next to each size.
- Let your partner measure the same pieces again, without looking at your sheet.
Safely: Lay the objects flat on the table to measure them. A caliper has pointed jaws: keep them away from your eyes and close them gently, not on your fingers.
Test it
Compare your two lists. If you differ by more than 1 mm on the same piece, measure again together and find where it went wrong, for example at the zero of the ruler. You also see straight away how many of the ten pieces are within the tolerance.
Pitfalls
Wrong: I put the end of my ruler against the edge and read it off.
On many rulers the zero is not right at the end. Then you measure a few millimetres too little every time.
Right: Put the zero line exactly against the edge of the object and look straight down at the scale.
Wrong: For 20 ± 0.1 mm, only exactly 20 mm is right.
No part is exactly 20 mm. The tolerance says precisely how much difference is allowed.
Right: Everything from 19.9 mm up to and including 20.1 mm is approved.
Wrong: On the caliper I guess the tenths of a millimetre by eye.
Guessing is imprecise. The vernier is there to read the tenths exactly.
Right: Read the whole millimetres on the main scale, then find the vernier line that lines up exactly with the main scale.
Wrong: I just write 2.5, everyone knows what I mean.
2.5 mm, 2.5 cm and 2.5 m are very different sizes.
Right: Always write the unit. Only on a technical drawing do you leave it out, because everything there is in millimetres.
In real life
- An AA battery fits every device that takes one, because the makers keep to the same sizes and tolerances.
- A joiner measures an alcove to the millimetre with a tape measure before building a made-to-measure cupboard into it.
- At the garage a mechanic uses a caliper to measure how thick a brake disc still is. If it is thinner than allowed, it has to be replaced.
History
In the 16th century the Portuguese mathematician Pedro Nunes came up with a way to read fractions of a scale division on a measuring instrument. The name nonius comes from him. The scale as it appears on a caliper today was described in the 17th century by the French mathematician Pierre Vernier. That is why it is called a vernier in French and English.
More in Ruit
Converting between millimetres, centimetres and metres and calculating with decimals is something you also practise in Ruit.
To RuitAt the table
Measure something at home with a tape measure, each of you separately. Do you get exactly the same size, and how big is the difference?
A question to talk about together, for parents and children. There is no wrong answer.