What is a Tolerance Stack-Up?
A tolerance stack-up is a calculation that predicts how individual part tolerances combine to affect a critical assembly dimension. It answers the question every engineer needs to know before production: "Will this fit?"
The Basic Concept
No part is ever made exactly to its nominal dimension. A shaft specified as 10.00mm might actually measure 9.98mm or 10.02mm. A hole might be 10.05mm or 9.95mm. These variations are expected and controlled by tolerances.
The problem arises when you assemble multiple parts. Each part brings its own variation. A tolerance stack-up traces how these individual variations accumulate (stack up) along a path through the assembly.
Simple Example
A shaft (10.00 ±0.05mm) fits into a hole (10.10 ±0.05mm). The nominal clearance is 0.10mm. But what's the minimum clearance? If the shaft is at maximum (10.05mm) and the hole is at minimum (10.05mm), the clearance is zero—they bind. A stack-up calculation reveals this before you build hardware.
Closed Loop vs. Open Loop
A tolerance stack-up follows a dimension chain—a path through the assembly connecting two surfaces or features. There are two types:
Closed Loop (Gap Analysis)
The dimension chain forms a complete loop back to the starting point. You're calculating an internal gap, clearance, or interference. The sum of all dimensions around the loop must equal zero (gaps are the "closing" dimension).
Example: Clearance between a bearing and a housing shoulder—the loop passes through the bearing, shaft, housing, and back to the bearing.
Open Loop (External Dimension)
The dimension chain has distinct start and end points. You're calculating an overall length, height, or position. There's no internal gap—just the accumulated dimension.
Example: Total height of a stacked assembly—sum of all component heights.
WC vs. RSS: Two Analysis Methods
Once you have your dimension chain, you need to calculate the total variation. There are two standard methods:
Worst-Case (WC)
Assumes every dimension hits its worst limit simultaneously. Conservative—if WC passes, 100% of assemblies will work.
Root Sum Squares (RSS)
Statistical approach—assumes tolerances won't all hit extremes. Tighter results but some small fallout expected.
Most engineers run both analyses. If WC passes, you're done—design is robust. If WC fails but RSS passes, you may accept statistical risk depending on volume and criticality.
Read the full WC vs. RSS guide →
When Do You Need a Stack-Up?
You need a tolerance stack-up when:
- Multiple parts contribute to a critical dimension — Any gap, fit, or clearance involving 3+ features
- Failure has consequences — Binding, leakage, misalignment, or performance degradation
- You're releasing drawings for production — Validate tolerances before committing to tooling
- Design review requires evidence — Prove your design works, don't just assert it
- You're troubleshooting assembly problems — Find which dimensions are driving failures
When to Create a Formal Report
Quick scratch-paper stack-ups are fine for early estimates. But you need a formal tolerance report when:
- The analysis will be reviewed by others (peers, management, customers)
- You need documented evidence for a design review
- The product is in a regulated industry (aerospace, medical, automotive)
- You'll revisit the analysis months later and need to understand assumptions
- You're communicating tolerance requirements to suppliers
Learn what to include in a tolerance report →
Common Mistakes Beginners Make
- Missing dimensions — Forgetting a contributor makes results optimistic
- Wrong signs — Confusing which dimensions add vs. subtract from the gap
- Using RSS without justification — Statistical analysis requires volume and process capability
- Ignoring GD&T — Position, profile, and other callouts contribute to stacks
- Not documenting assumptions — Temperature, material, and process assumptions matter
Summary
A tolerance stack-up is a fundamental engineering calculation that predicts how manufacturing variation affects your assembly. It traces a dimension chain through contributing features, calculates the combined tolerance (using WC or RSS), and compares the result to your functional requirements.
When the analysis is important enough to share or archive, document it in a formal tolerance report.