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Tolerance is something that is unintended measurement... whereas allowance is one that we give to the material to undergo some process in the future.... For example a cylindrical bore is done undersize to allow honing process in the future,,, and at the final operation we check whether the final size is in the given upper and lower tolerance limits... over tolerance is unintended and we process the material for average size as far as possible.

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Mathematically:

Tolerance = |MMC - LMC|

Allowance = MMC(interior) - MMC(exterior)

MMC - Maximum Material Condition; instance of feature dimensions that gives maximum volume, consistent with tolerances.

LMC - Least Material Condition; instance of feature dimensions that gives least volume, consistent with tolerances.

Interior - A hole is an interior feature

Exterior - A shaft is an exterior feature

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