tolerances

Tolerances are the permissible deviations from a defined standard or target value. In engineering, manufacturing, and metrology, tolerances specify how much a part's dimensions or performance characteristics may vary while still meeting requirements. They balance functional needs, interchangeability, and the realities of production, where deviations arise from material behavior, tooling, and measurement limitations.

Dimensional tolerances constrain size and location, expressed as a nominal dimension plus a tolerance interval, for example 50.00 mm with a tolerance of ±0.05 mm. Geometric tolerances specify the allowable variation in form, orientation, and runout, using symbols and datum references. Tolerances can be unilateral (deviation allowed on one side only) or bilateral (on both sides). The term 'tolerance zone' describes the region within which the feature must lie.

Tolerance analysis evaluates how individual tolerances affect overall assembly performance. Worst-case analysis considers all deviations at their extremes, while statistical or RSS methods model more probable combinations. Tolerance stack-up is the cumulative effect of multiple tolerances along an assembly, driving design choices and manufacturing costs. Standards such as ISO 286 for limits and fits and ASME Y14.5 for geometric tolerancing govern specification practice.

Alongside engineering, tolerances describe biological and ecological limits, namely the range of environmental conditions an organism or system can withstand. In social contexts, tolerance denotes acceptance of diverse views or behaviors within a group. Across domains, tolerances govern quality, safety, compatibility, and resilience by defining acceptable variation.