Tolerance stacks

Tolerance Analysis is the general term for all activities related to the study of accumulated variation in mechanical parts and assemblies, and may be used on other types of systems subject to accumulated variation, such as mechanical & electrical systems.

Tolerance stacks, Tolerance stackups or tolerance stack-ups are terms used to describe the problem-solving process in mechanical engineering of calculating the effects of the accumulated variation that is allowed by specified dimensions and tolerances. Typically these dimensions and tolerances are specified on an engineering drawing. Arithmetic tolerance stackups use the worst-case maximum or minimum values of dimensions and tolerances to calculate the maximum and minimum distance (clearance or interference) between two features or parts. Statistical tolerance stackups evaluate the maximum and minimum values based on the absolute arithmetic calculation combined with some method for establishing likelihood of obtaining the maximum and minimum values, such as Root Sum Square (RSS) or Monte-Carlo methods.

While no official engineering standard covers the process or format of tolerance analysis, tolerance analysis and tolerance stackups are essential components of good product design. Tolerance stackups should be used as part of the mechanical design process, both as a predictive tool and as a problem-solving tool. The methods used to conduct a tolerance stackup depend somewhat upon the engineering dimensioning and tolerancing standards that are referenced in the engineering documentation, such as ASME Y14.5, ASME Y14.41, or the relevant ISO dimensioning and tolerancing standards. Understanding the tolerances, concepts, and boundaries created by these standards is vital to performing accurate calculations.

Tolerance stackups serve engineers by:

  • helping engineers and designers study dimensional relationships within an assembly
  • giving designers a means of calculating part tolerances
  • helping engineers compare design proposals
  • helping designers produce complete drawings


An important aspect of performing tolerance stackups is the documentation. The calculations need to be available for multiple engineers, designers and suppliers in industrial applications. Therefore good documentation practices are vital to using a stackup calculation. A tolerance stackup form, and a tolerance stackup sketch are frequently used documentation practices. If a tolerance stackup is not properly documented, the results will be difficult to understand and it will be difficult to verify that the problem was modeled correctly.

Concerns with tolerance stackups

A safety factor is often included in designs because of concerns about:

  • Operational temperature of the parts or assembly
  • Wear
  • Deflection of components after assembly
  • The possibility or probability that the parts are slightly out of specification (but passed inspection)
  • The sensitivity or importance of the stack (what happens if the design conditions are not met)


  • ASME journal publication (2003). "Automation of Linear Tolerance Charts and Extension to Statistical Tolerance Analysis". Journal of Computing and Information Science in Engineering 3 (1): 95–99.
  • ASME publication Y14.41-2003, Digital Product Definition Data Practices
  • Alex Krulikowski (1994), Tolerance Stacks using GD&T, ISBN 0-924520-05-1
  • Bryan R. Fischer (2004), ''Mechanical Tolerance Stackup and Analysis", ISBN 0-8247-5379-8

External references

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