Tolerance Stack-Up Calculator: How WC and RSS Analysis Work
A tolerance stack-up calculator helps mechanical engineers predict whether assembled parts will fit and function correctly. Learn how worst-case and RSS analysis work, when to use each method, and how to document your analysis for design reviews.
What Is a Tolerance Stack-Up?
A tolerance stack-up (also called tolerance analysis or tolerance chain) calculates the cumulative effect of individual part tolerances on an assembly's critical dimensions. When multiple parts stack together, their tolerances combine—sometimes adding up to unacceptable variation.
For example, if you have a shaft running through three bearings, each bearing's position tolerance contributes to the total alignment error. A tolerance stack-up calculator helps you predict the worst-case scenario and statistical likelihood of fit issues before you build hardware.
Two Methods: Worst-Case vs. RSS
Mechanical engineers use two primary methods for 1D tolerance stack-up analysis:
Worst-Case (WC) Analysis
Worst-case analysis assumes every dimension is at its extreme limit simultaneously. The formula is simple:
When to use WC: Safety-critical assemblies, low-volume production, or when 100% interchangeability is required. If the worst-case stack passes, every assembly will work.
Root Sum of Squares (RSS) Analysis
RSS analysis uses statistical probability, assuming tolerances follow a normal distribution and won't all be at their limits simultaneously:
When to use RSS: High-volume production where statistical averaging occurs, or when WC tolerances would make parts too expensive to manufacture.
Learn more in our guide: Worst-Case vs. RSS: When to Use Each Method
How to Perform a Tolerance Stack-Up
- Identify the critical dimension — What gap, clearance, or alignment matters for function?
- Build the dimension chain — List every dimension that contributes to the stack, from one reference to another
- Assign directions — Mark each dimension as positive (adds to gap) or negative (subtracts from gap)
- Enter nominals and tolerances — Use bilateral tolerances (±) from your drawings
- Calculate results — Compute WC and RSS min/max values
- Document assumptions — Record what you assumed (no thermal expansion, parts in spec, etc.)
See a worked example: Tolerance Stack-Up Example: Clevis Pin Assembly
Why Spreadsheets Fall Short
Many engineers build tolerance stack-ups in Excel. While spreadsheets work for calculations, they create problems:
- Formulas break when rows are added or deleted
- No standard format for design reviews
- Assumptions aren't documented
- Hard to compare revisions
- PDFs from Excel look unprofessional
Read more: Why Excel Templates Fail for Tolerance Stack-Ups
Sensitivity Analysis: Find Your Biggest Contributors
A good tolerance calculator shows which dimensions contribute most to your stack variation. This sensitivity analysis helps you:
- Focus tolerance tightening where it matters
- Justify premium manufacturing costs
- Identify dimensions to inspect more carefully
The sensitivity formula for each dimension is:
What Makes a Good Stack-Up Report?
Design reviews require clear documentation. A professional tolerance stack-up report includes:
- Project name and revision
- Assembly target (min/max acceptable values)
- All dimensions with nominals and tolerances
- Direction signs (+ or −)
- WC and RSS results with pass/fail status
- Sensitivity chart showing top contributors
- Documented assumptions
Frequently Asked Questions
What's the difference between 1D and 3D tolerance analysis?
1D analysis handles linear dimension chains (what TolReport does). 3D analysis uses CAD software to simulate complex geometric relationships. For most mechanical assemblies, 1D analysis is sufficient and much faster.
Should I use WC or RSS tolerances?
Use worst-case for safety-critical or low-volume assemblies. Use RSS for high-volume production. Many engineers run both and compare results. Learn more →
How do I handle GD&T in a stack-up?
Convert GD&T callouts to equivalent bilateral tolerances. Position tolerances become ± half the diameter zone. Profile tolerances convert similarly based on the feature.
Can I use TolReport for free?
Yes. The free tier includes up to 3 saved projects with full WC/RSS analysis and sensitivity charts. Try it now →