Tolerance Stack Calculator
Stack tolerance (±)
0.014
How it works
Tolerance stack-up analysis determines the worst-case variation in an assembly when multiple components, each with dimensional tolerances, fit together. Understanding stack-up prevents interference fits and excessive gaps in assembled mechanisms.
**Worst-case analysis** Worst-case stack-up: simply sum all individual tolerances. If three gaps are each 10 ± 0.1 mm, the total gap is 30 mm, but could range from 29.7 to 30.3 mm (worst case). This is conservative — useful for safety-critical applications where any combination of dimensions must work.
**Statistical stack-up (RSS method)** Root Sum Square (RSS): total tolerance = √(t₁² + t₂² + t₃² + ...). For three ±0.1 mm tolerances: RSS = ±√(0.1² + 0.1² + 0.1²) = ±0.173 mm. This represents ±3σ variation under normal distribution assumptions (if each tolerance represents ±3σ). RSS predicts what actually occurs in production better than worst-case.
**GD&T and feature-based stack analysis** Geometric Dimensioning and Tolerancing (GD&T) provides a framework for specifying tolerances that enable proper stack-up analysis. Position tolerance, form tolerance, and datum reference frames all affect how tolerances combine. Virtual condition (worst mating condition) is key to interference analysis.
**Tolerance allocation** Given an assembly requirement, allocate tolerances to individual components. Tighter tolerances cost more — allocate tighter tolerances to dimensions with large stack-up contributions and looser tolerances elsewhere. Components with high sensitivity (large partial derivatives in the stack-up equation) should receive tighter tolerances.
Frequently Asked Questions
- Worst-case: add all tolerances — guarantees every assembly works regardless of which extreme each part takes. Conservative and safe for small-quantity, high-reliability assemblies. Statistical (RSS): assumes each part takes a random value from its distribution — only ~0.27% of assemblies fall outside the RSS tolerance (for ±3σ). RSS gives a tighter assembly tolerance than worst-case (RSS tolerance = √Σt² vs. Σt). Use worst-case for: safety-critical assemblies, small production runs, assemblies where rejections are catastrophic. Use RSS for: high-volume production where some assembly variation is acceptable, and where 100% interchangeability isn't required.
- Sensitivity analysis: each dimension contributes to the total stack-up sensitivity based on its partial derivative in the stack-up equation. For a linear chain: all dimensions contribute equally (sensitivity = 1). For more complex geometry, sensitivities vary. The tolerance contribution = sensitivity × tolerance. Rank dimensions by tolerance contribution and tighten the largest contributors first. A dimension with sensitivity 2 and tolerance ±0.2 mm contributes the same as a dimension with sensitivity 1 and ±0.4 mm. Tightening a low-sensitivity dimension has little effect on assembly variation; focus on high-sensitivity, high-tolerance dimensions.
- GD&T position tolerance (⌀0.1 mm) defines a cylindrical zone within which the hole center must lie — the zone diameter is the position tolerance. For a clearance fit (bolt through hole): worst-case clearance = hole_min_size - bolt_max_size - position_tolerance_hole - position_tolerance_bolt. For a 10mm bolt through a 10.5mm hole, each with ⌀0.1mm position tolerance: minimum clearance = (10.5 - 0.1/2) - (10 + 0.1/2) - 0.1 - 0.1 = -0.05mm — interference possible in worst case. Correct by increasing hole size, reducing position tolerances, or using floating fasteners.
- Assembly gap is the air space between mating parts when all parts are assembled. Too large a gap: aesthetic problem, structural weakness, rattling. Too small (or negative) gap: interference, parts won't assemble. Tolerance stack-up predicts the gap distribution. For a stack-up with nominal gap G₀ = 2mm and total tolerance T: gap ranges from G₀ - T to G₀ + T (worst-case). To ensure gap is always positive: G₀ > T (nominal gap must exceed total tolerance). Solve interference problems by: increasing nominal gap, tightening individual tolerances, using shims for adjustment, or designing for adjustability (slotted holes, adjustment screws).