Method / Worked guide

Write the closure.
Keep both endpoints.

This tool evaluates one signed sum of dimensional intervals. It answers what range follows from that arithmetic model and the limits you entered.

1. Turn a nominal size into a closed interval

For a nominal size a, lower deviation l and upper deviation u, the physical size interval is [a−l, a+u]. The deviations are nonnegative magnitudes. They need not be equal. A lower deviation of 0 means the nominal is already the physical lower limit. These inputs are dimensional limits supplied by you; they do not describe a probability distribution.

For example, a 70 mm nominal with lower deviation 1 mm and upper deviation 2 mm gives [69,72] mm. If this size is added in the closure, its signed contribution is unchanged. If it is subtracted, the contribution is [−72,−69] mm. The most negative contribution comes from subtracting the largest physical size. Negating both numbers without reversing their order would make an invalid descending interval.

The nominal signed sum is calculated separately. It lies within the resulting interval, but asymmetric deviations need not put it at the interval's midpoint. A negative signed result is an offset in the direction opposite to the one you defined; it does not imply that any individual physical size is negative.

2. Housing minus insert minus spacer

Suppose your chosen linear closure is housing size minus insert size minus spacer size. This is an arithmetic illustration, with no assumption about a particular manufactured fit or safe assembly. Enter these three separate rows in millimetres:

The nominal result is 100−60−39=1 mm. For the minimum, use the housing's smallest value and subtract the insert and spacer's largest values:99.8−60.2−39.1=0.5 mm. For the maximum, use the housing's largest value and subtract the other two smallest values:100.3−59.9−38.9=1.5 mm. The closed result interval is therefore[0.5,1.5] mm, with width 1 mm.

Adding each contributor's interval width gives the same total:0.5+0.3+0.2=1 mm. Subtracting a dimension reverses its endpoint contributions, but its width still adds to the envelope's width. Opposing signs do not cancel independent interval widths.

3. Check the answer by enumerating endpoint corners

Three separate two-endpoint rows have eight endpoint combinations. A small corner table gives an independent way to check the endpoint-sum equations:

The smallest corner is 0.5 and the largest is 1.5. The table lists possible arithmetic corner combinations under the separate-interval model. It assigns no frequency, likelihood or population proportion to any row.

4. Compare the whole interval with your entered criterion

The optional criterion is another closed interval[A,B]. Enter both endpoints or leave both blank. Blank is not interpreted as zero. The entire result[L,U] is contained exactly whenL≥A andU≤B. Equality is included at each boundary.

For the example result[0.5,1.5], an entered criterion[0.6,1.4] does not contain the entire envelope. The lower margin isL−A=−0.1 mm, and the upper margin isB−U=−0.1 mm. A negative margin identifies the direction and distance of an exceeded bound. It does not predict a rejection rate. If you enter[0.5,1.5] instead, both margins are zero and containment is true.

A zero-width result is valid: when every deviation is zero, both endpoints equal the nominal signed sum. A zero-width criterion is also valid, but contains the result only when that result is the same single point. The tool does not invent a minimum width or a tolerance for a near-equality comparison.

5. Keep physical values through unit changes

The international inch is exactly 25.4 mm. Stackrange keeps an exact rational millimetre value for each separate numeric field. Selecting inches changes its displayed text while retaining the unedited physical value. A field can display at most 12 fractional places, so a converted value may be rounded for presentation. An exact-value notice explains this state.

Editing a numeric field intentionally replaces only that field's cached physical value with the value now typed in the selected unit. Editing a label or add/subtract selector leaves all numeric values intact. Repeated mm/in switches do not repeatedly reinterpret rounded text. This matters for a criterion endpoint exactly equal to a result bound, or a very small deviation that rounds to zero in the other unit.

If a required numeric field has incomplete syntax, the unit switch is stopped and the previous unit restored. A semantically invalid but well-formed value, such as an excessive lower deviation, can still be converted while the model remains rejected. A partially entered criterion remains invalid until both endpoints are supplied or both cleared.

6. Read exact and rounded values together

Primary numeric views are rounded to at most 12 decimal places. Exact fractions accompany the result bounds, nominal and width; the endpoint table and local reports preserve exact values. Canonical millimetre fractions are included in the reports so the model can be checked independently of a later unit display.

The diagram shows the closed computed interval, nominal marker and optional criterion outline. Its drawing coordinates are rounded. It is a schematic interval view, with no density curve, sample histogram or inferred distribution. Very close bounds can coincide visually; the exact table and margins remain the arithmetic reference.

Labels are plain text and do not execute as markup. Text reports quote labels. CSV quotes its fields and prefixes a label that looks like a spreadsheet formula with an apostrophe so it is exported as literal text. Spreadsheet applications can also reinterpret fraction strings as dates or numbers; import exact-value columns as text if literal preservation matters.

7. The closure and interval assumptions matter

You define the add/subtract relation. The tool does not import CAD, determine a valid dimensional loop or check physical assembly geometry. It omits rotations, angles, lever arms, form, datum and material modifiers, deformation, thermal changes and assembly shift. It does not look up ISO or ASME fit classes or certify a component.

Each row is a separate interval contributor. If two rows refer to the very same underlying variable, its correlation is not represented. For example, entering the same uncertain dimension once added and once subtracted produces a conservative interval width here, even though an algebraically identical shared variable would cancel exactly. The model cannot identify that repeated relationship from labels. Actual assembly constraints may also prevent the chosen individual extremes from occurring together.

No RSS, Monte Carlo, normality, Cpk, yield, defect-rate, reliability or measurement-uncertainty model is implemented. An envelope follows from entered bounds; it does not validate their measurement accuracy, decide whether the model suits a real process or establish a safety/compliance conclusion.

Software limits

Use 1–30 contributors. Each nominal and each deviation is nonnegative and bounded by 1,000,000 mm equivalent. The lower deviation cannot exceed its nominal. The largest physical upper endpoint can therefore be 2,000,000 mm. Thirty such contributors give an overall possible magnitude of 60,000,000 mm; both optional signed criterion endpoints use that software bound.

Inputs are plain decimals with at most 12 fractional places and 64 characters per numeric field. Exponents and unit suffixes reject. Optional labels are limited to 80 characters. These are practical browser-software bounds, not manufacturing recommendations. Restore example discards the current rows and returns the three illustrated contributors.

References

• Autodesk's official tolerance-analysis help distinguishes extreme-limit worst-case analysis from statistical approaches. Stackrange implements only its own one-dimensional interval arithmetic, with none of that product's CAD or GD&T capabilities.
• NIST's length-unit reference supplies the exact international-inch relationship. No fit-class standard is implied.

The formulas, examples, interface and code here are original. Calculations and downloads stay local; the privacy notice describes ordinary hosting and the current inactive ad/analytics configuration.