Limit dimensions calculator

What it computes

A toleranced size can be written three ways: as limits (25.021 / 25.000), as a nominal with deviations (25 +0.021 / 0), or as a nominal with a symmetric tolerance (25 ±0.01). Each form states the largest and the smallest acceptable size. The calculator turns the second and third forms into the first. It also gives the two figures that fits and stack-ups use: the tolerance band and the mean size.

Formulas

• Upper limit = nominal + upper deviation.
• Lower limit = nominal + lower deviation.
• Tolerance band = upper deviation − lower deviation.
• Mean (mid-limit) size = nominal + (upper deviation + lower deviation) / 2.
• A symmetric ±t is an upper deviation of +t and a lower deviation of −t.

Conventions

Deviations are signed. ISO 286-1 calls them the upper and lower limit deviations and measures both from the nominal size. Both can be negative: a shaft toleranced −0.007 / −0.020 is smaller than nominal at either limit. Both can be positive, as with a hole at +0.040 / +0.020.

The upper deviation must not be below the lower one. The calculator refuses that input instead of swapping the values, because a swapped pair is often a sign error that needs a second look.

A ± tolerance is entered as its size, 0.05 for ±0.05. A negative value is refused. A tolerance of zero is accepted and flagged, since no process makes a size exactly.

One unit covers every value in a calculation. If the nominal is in inches, the deviations are in inches too. Convert first with the unit converter if the drawing mixes units. The nominal and the lower limit must be greater than zero, because a size cannot be zero or negative.

ASME Y14.5 describes limit dimensioning and plus and minus tolerancing. ISO 286-1 defines the vocabulary of sizes and deviations. The arithmetic here is the same under either standard.

Exact arithmetic and display precision

The calculator adds the decimals you typed exactly, so 80.3 + 0.1 is 80.4 and not 80.39999999999999. Rounding happens only in the displayed figures, to the number of decimals you choose: three for millimetres and four for inches by default. When rounding hides a digit, the full value is shown underneath. A mean of 25.0105 mm at three decimals shows as 25.011, with 25.0105 beside it.

Worked example

Limitations

• Sizes only. It does not handle angular tolerances, and it does not interpret geometric tolerances or form requirements that apply on top of the size limits.
• It does not look up ISO 286 tolerance classes. For a class such as H7, take the deviations from ISO 286-2 or from the drawing.
• It does not judge whether a band is achievable or economical for a given process.
• Values take a decimal point, not a comma, and at most 15 significant digits.

When to involve a qualified engineer

Ask the engineer who owns the drawing when a callout is ambiguous, when the deviations look reversed, or when a size has a band of zero. Ask before you tighten or loosen a limit to suit a process, too. A limit is part of the design, not a shop setting.