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What is tolerance, and how do engineers use upper and lower limits to control accuracy?

Tolerance and dimensional accuracy: nominal size, upper and lower limits, and calculating the tolerance of a dimension.

A CCEA GCSE Engineering and Manufacturing answer on tolerance and dimensional accuracy, covering nominal size, upper and lower limits, calculating tolerance, and why tolerances let parts be made and fit together.

Generated by Claude Opus 4.811 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

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  1. What this dot point is asking
  2. The answer
  3. Examples in context
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What this dot point is asking

CCEA Unit 3 expects you to understand tolerance: the nominal size, the upper and lower limits, how to calculate the tolerance, and why tolerances are used. This is a calculation as well as an explanation topic.

The answer

What tolerance is

Tolerances are written as the nominal size with a deviation, for example 25±0.2 mm25 \pm 0.2\ \text{mm}, meaning the part is acceptable between 24.8 mm and 25.2 mm.

Why tolerances are needed

Calculating limits and tolerance

For a dimension given as nominal ±\pm deviation:

  • Upper limit = nominal + deviation
  • Lower limit = nominal - deviation
  • Tolerance = upper limit - lower limit

A measured part is acceptable only if its size lies between the lower and upper limits inclusive.

Worked example: a tolerance calculation

Examples in context

Example 1. A shaft and bearing
Both are given tolerances so the shaft is always slightly smaller than the bore by a controlled amount, guaranteeing they fit together every time without being made to one impossible exact size.
Example 2. Mass-produced parts
Tolerances let thousands of parts be made on different machines and still assemble correctly, because each is within the allowed range (interchangeability).
Example 3. Cost control
A designer sets a wider tolerance where accuracy does not matter, because a tighter tolerance would raise cost and rejects for no benefit.

The pattern is that tolerances make real manufacture possible: parts vary, but a controlled range guarantees fit and function while keeping cost reasonable.

Try this

Q1. A part is dimensioned 30±0.1 mm30 \pm 0.1\ \text{mm}. State the upper and lower limits. [2 marks]

  • Cue. Upper limit 30.1 mm; lower limit 29.9 mm.

Q2. Calculate the total tolerance for 30±0.1 mm30 \pm 0.1\ \text{mm}. [1 mark]

  • Cue. Tolerance =30.1−29.9=0.2 mm= 30.1 - 29.9 = 0.2\ \text{mm}.

Q3. Why are tolerances used instead of one exact size? [2 marks]

  • Cue. No process makes every part exactly the same, so a usable range is allowed so parts still fit and work without being rejected.

Exam-style practice questions

Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

CCEA style4 marksA shaft is dimensioned 25 mm plus or minus 0.2 mm. State the upper limit, the lower limit and the total tolerance, and say whether a measured shaft of 25.3 mm is acceptable.
Show worked answer →

The nominal size is 25 mm and the deviation is plus or minus 0.2 mm.

Upper limit =25+0.2=25.2 mm.= 25 + 0.2 = 25.2\ \text{mm}.

Lower limit =25−0.2=24.8 mm.= 25 - 0.2 = 24.8\ \text{mm}.

Total tolerance =25.2−24.8=0.4 mm.= 25.2 - 24.8 = 0.4\ \text{mm}.

A shaft measured at 25.3 mm is too big (above the 25.2 mm upper limit), so it is outside tolerance and rejected.

Markers reward the upper limit (25.2), lower limit (24.8), tolerance (0.4 mm) and the conclusion that 25.3 mm is rejected because it exceeds the upper limit.

CCEA style3 marksExplain why parts are given a tolerance rather than one exact size, and what happens if a tolerance is made too tight.
Show worked answer →

Parts are given a tolerance because it is impossible to make every part exactly the same size; there will always be small variations. A tolerance gives an allowed range within which the part still works and fits, so usable parts are not rejected.

If a tolerance is made too tight (too small a range), the part is harder and more expensive to make, more parts are rejected, and production slows, raising cost. Tolerances should be only as tight as the function needs.

Markers reward the idea that exact sizes are impossible so a usable range is allowed, and that tighter tolerances raise cost and rejects.

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