The Problem

Every dimension on a drawing has a tolerance. When parts assemble together, those tolerances add up — or “stack.” A stack-up analysis tells you whether your assembly will work in the worst case, or if you’ll be forcing parts together on the shop floor.

A Simple Example

You have a shaft that fits into a hole:

  • Hole: 1.000″ ±0.005″ (range: 0.995″ – 1.005″)
  • Shaft: 0.998″ ±0.003″ (range: 0.995″ – 1.001″)

Best case: Hole = 1.005″, Shaft = 0.995″ → 0.010″ clearance. Easy.

Worst case: Hole = 0.995″, Shaft = 1.001″ → interference fit. Won’t assemble.

Your drawing says it fits. Reality says 25% of the time, it won’t.

Worst-Case (Arithmetic) Stack-Up

Add up all tolerances at their extremes. This guarantees 100% of assemblies work, but it’s pessimistic — the chance of EVERY part being at its worst extreme simultaneously is near zero.

Total tolerance = sum of individual tolerances

Use when: failure is catastrophic (safety-critical, aerospace, medical).

Statistical (RSS) Stack-Up

Root Sum Square method assumes dimensions follow a normal distribution. The combined tolerance is smaller than worst-case:

Total tolerance = √(t₁² + t₂² + t₃² + …)

For three tolerances of ±0.005″ each:

  • Worst-case: ±0.015″ total
  • RSS: ±0.0087″ total

Use when: statistical defects are acceptable (consumer products, non-critical assemblies). Assumes ~99.7% yield (3σ).

Common Stack-Up Problems

Hole Pattern Misalignment

Four bolt holes on Part A mate to four holes on Part B. Each hole has ±0.005″ position tolerance. Worst case: holes could be 0.020″ off from each other. Solution: larger clearance holes, or tighter position tolerance on one part.

Multi-Part Assemblies

A stack of 5 shims, each 0.100″ ±0.003″. Worst case: 0.500″ ±0.015″. RSS: 0.500″ ±0.0067″. If the slot is 0.510″ ±0.005″, worst-case analysis says it might not fit.

Chain Dimensions

Dimensioning from feature to feature to feature creates a chain. Each link adds tolerance. Dimensioning everything from a single datum minimizes stack-up.

How to Fix It

  • Tighten critical tolerances — but only where the stack-up demands it (costs money)
  • Add clearance — make holes bigger, add gaps, use floating fasteners
  • Use datums wisely — dimension from one reference surface instead of chaining
  • Design in adjustability — slots instead of holes, shims, set screws
  • Match-machine — machine mating features together in the same setup

The Real-World Rule

If your assembly requires every part to be at nominal to work, your design is broken. Good designs work even when every part is at the edge of its tolerance band. That’s what tolerance stack-up analysis ensures.

Need help with fit and tolerance? Send us your assembly drawing — we’ll review the stack-up before we cut metal.