Tolerances and Fits - CourseWiki

A size tolerance gives two limits

Manufacturing produces variation. For each diameter in this lab, the drawing gives a size between two limits. A measured diameter inside that interval passes this size check.

Nominal size: The size a feature is named by, such as Ø0.7500 in. Ø means diameter. Every limit is measured from this number.
Deviation: How far a limit sits above (+) or below (−) nominal. +0.0010 puts a limit 0.0010 in above it.
Limits: Nominal plus each deviation: the largest and smallest sizes that pass inspection. Ø0.7500 +0.0010 / 0.0000 means anything from 0.7500 in to 0.7510 in.
Tolerance: The width of that range: largest limit minus smallest limit. Here, 0.0010 in.

A size exactly on a limit passes. On this page the limits are part of the allowed range: a 0.7500 in hole and a 0.7510 in hole are both good. A 0.7511 in hole is not.

Clearance is the hole size minus the shaft size

Put a shaft in a hole and the number that decides the fit is the difference between their two diameters.

clearance = hole size − shaft size

Positive: the hole is bigger. There is a gap, and the shaft slides in.
Negative: the shaft is bigger. That is interference: on paper the parts overlap, so the shaft has to be pressed in, or it does not go at all.
Zero: exactly the same size, called line-to-line. No gap and no overlap.

Clearance is measured across the whole diameter. With the shaft centred in the hole, the gap you would see on each side is half of it:

gap on each side = clearance ÷ 2

The gap is drawn hugely enlarged. At the size of this drawing, a 0.00025 in gap would be far too thin to see. Hatching marks the cut face of the block.

Three kinds of fit, decided by the two worst cases

You do not have to check every pair of parts a drawing allows. Two pairs settle it: the tightest and the loosest.

Tightest legal pair: The smallest hole with the largest shaft. Its clearance is the least any good pair can have:
hole minimum − shaft maximum
Loosest legal pair: The largest hole with the smallest shaft. Its clearance is the most any good pair can have:
hole maximum − shaft minimum

The fit is named by where those two numbers land.
Fit	Tightest pair	Loosest pair	What it means
Clearance	gap, or exactly zero	gap	No permitted pair has dimensional overlap. Equality has no gap.
Transition	overlap	gap	Some good pairs slide together; some have to be pressed.
Interference	overlap	overlap, or exactly zero	No permitted pair has a positive gap. Equality has no overlap.

The zero cases are deliberate. When the tightest pair comes out at exactly zero, every good pair either has a gap or just meets, so this page counts it as a clearance fit and the lab marks it zero at the limit. The same goes the other way for interference.

Higher means bigger. Each box is the range of sizes one part may have; the dashed line is the nominal size. The hatched band in the middle panel is the range of sizes both parts are allowed to have, which is what makes an overlap possible.

Fit lab: make two parts, then try them together; Interactive

Fit lab: make two parts, then try them together

Pick a drawing, then set the size each part actually came out at. Watch whether each part passes inspection, and whether the two go together.

The section view is the pair you made, cut in half. The gold and blue bands are where each wall is allowed to be.
The pair map is every pair the drawing allows. Anything above the diagonal has a shaft bigger than its hole.

The lab’s example drawings. All are made-up teaching limits on a Ø0.7500 in nominal, not values from any standard.
Drawing	Hole limits	Shaft limits	Tightest pair	Loosest pair	Fit
Slides freely	0.7500 to 0.7510	0.7480 to 0.7490	+0.0010	+0.0030	Clearance
Could go either way	0.7500 to 0.7510	0.7498 to 0.7506	−0.0006	+0.0012	Transition
Pressed together	0.7500 to 0.7510	0.7515 to 0.7525	−0.0025	−0.0005	Interference

Two good parts can still make a bad pair; Watch out

Two good parts can still make a bad pair

Checking each diameter against its own limits does not by itself check the clearance of the selected pair.

Take the transition drawing from the lab: holes from 0.7500 to 0.7510 in, shafts from 0.7498 to 0.7506 in.

Hole made at 0.7502: Inside 0.7500 to 0.7510. Passes.
Shaft made at 0.7505: Inside 0.7498 to 0.7506. Passes.
Together: 0.7502 − 0.7505 = −0.0003 in. The shaft is bigger than the hole. They overlap.

Neither part is wrong. The drawing allows that pair, and that is what transition fit allows. To exclude dimensional overlap for every permitted pair, the tightest pair must have zero clearance or more. To guarantee a positive dimensional gap, it must be greater than zero. Neither check by itself guarantees assembly: shape, surface finish, temperature and the assembly method also matter.

Call the fit from the drawing alone; Interactive

Call the fit from the drawing alone

Read the two callouts, work out the tightest and loosest pairs, and call it before you look.

Five drawings, each on a Ø0.7500 in nominal. Work out the limits, then the tightest and loosest pairs. The answer follows each one.

Hole +0.0012 / 0.0000, shaft −0.0004 / −0.0011. Clearance: +0.0004 to +0.0023.
Hole +0.0008 / 0.0000, shaft +0.0010 / +0.0003. Transition: −0.0010 to +0.0005.
Hole +0.0006 / 0.0000, shaft +0.0018 / +0.0012. Interference: −0.0018 to −0.0006.
Hole +0.0010 / 0.0000, shaft 0.0000 / −0.0007. Clearance, zero at the limit: 0.0000 to +0.0017.
Hole +0.0015 / +0.0005, shaft +0.0007 / −0.0003. Transition: −0.0002 to +0.0018.

What this lab leaves out

The lab compares two diameters and nothing else. A real assembly also depends on:

Shape. No hole is perfectly round or straight, and no shaft is either. A shaft can measure in tolerance everywhere a micrometer touches it and still be bent too far to go in.
Temperature. Parts grow when they warm up, so the same part can measure differently straight off the machine and an hour later.
Surface finish and measurement. A rough surface and an imperfect measurement both blur the last decimal place the drawing asks for.
Force. Whether an interference pair can be pressed together, how hard, and what that does to the parts are questions about the material, not about the two sizes.

The limits in the lab are made-up teaching values. Real drawings often take limits from published tables of standard fits; those tables are not reproduced here.

For measuring a real part, start with choosing a measuring tool, reading its scale, and checking the measurement method. See Shop Layout and Angle Measurement for transferring dimensions onto the work.