Stack Up Tolerance Analysis: Worst Case and RSS Methods
Build a one-dimensional assembly dimension chain, calculate worst-case minimum and maximum limits, and compare Root Sum Square (RSS) tolerance estimates. Identify controlling dimensions and check the resulting assembly gap against your requirements.
Build a signed dimensional chain and compare Worst Case with RSS estimates.
Tolerance Stackup Calculator
Enter nominal dimensions and signed lower/upper tolerance deviations.
| # | Dimension / feature | Direction | Nominal (mm) |
Lower dev. (mm) |
Upper dev. (mm) |
Remove |
|---|
For ±0.10 mm enter lower −0.10 and upper +0.10. For +0.10/0.00 mm enter lower 0 and upper +0.10. The direction sets the dimension’s sign in the assembly chain.
Worst Case Tolerance Stack Up
Guaranteed extreme sum if each entered dimension stays within its limits and the 1D chain model is complete.
0.0000 to 0.4000 mm
Enter requirement limitsRSS Tolerance Stack Up Calculator
Illustrative Root Sum Square estimate for independent, centered inputs with a common tolerance-to-sigma convention.
0.0775 to 0.3225 mm
Estimate onlyTolerance Analysis Calculator: Contribution Breakdown
Identify dimensions that dominate the worst-case sum and RSS variance.
| Dimension | Signed nominal (mm) | Half-range (mm) | Worst-case share | RSS variance share |
|---|
Tolerance Stack Calculator: Calculation Method
Worst case tolerance stack up adds the extreme contributions of every part in the dimensional chain. A + dimension contributes its minimum to the assembly minimum; a − dimension contributes its maximum to the assembly minimum.
The root sum square tolerance calculator estimates a half-range from the square root of the sum of each dimension’s half-range squared. This RSS result is meaningful only when the inputs are independent and have comparable statistical coverage.
- Individual center = nominal + (lower deviation + upper deviation) / 2.
- Individual half-range = (upper deviation − lower deviation) / 2.
- Worst-case range = sum of signed individual minimum and maximum limits.
- RSS estimate = signed center sum ± √Σ(half-range²).
* RSS assumptions: Deviations describe comparable kσ ranges of independent, approximately centered dimensions. No yield, Cpk, defect probability or statistical confidence is inferred from drawing tolerances alone.
Stack Up Tolerance Analysis for Mechanical Assemblies
This tolerance stack calculator is for a linear closed dimension chain, such as axial clearance, a cover-to-housing gap, spacer assembly or locating shoulder chain. Recheck dimension direction and the physical datum path before using the result.
Worst-case analysis gives extreme size limits for the modeled dimensions. A basic RSS model can underestimate production variation when parts are correlated, off-center, non-normal or subject to common manufacturing shifts.
Not modeled: 2D/3D geometric tolerance effects, datum shifts, angular error, temperature, material compliance, stress, wear, and manufacturing process correlations.
Tolerance Stackup Calculator FAQ
How to calculate tolerance stack up?
Define the functional assembly dimension, build the complete closed dimensional path, set +/− signs, and calculate the signed nominal sum. For Worst Case, add each dimension’s worst lower and upper contributions. Compare the result with assembly requirements.
How to do a tolerance stack up?
Start from the assembly’s functional gap and identify every contributing dimension, in order. Set the direction of each dimension and enter nominal values plus deviations. Compare Worst Case limits with the requirement. For RSS, compute √Σ(half-range²) around the signed sum of tolerance-band midpoints, after validating statistical independence and process assumptions.
Why can RSS results differ from Worst Case?
Worst Case permits every part to land at its adverse limit simultaneously. RSS assumes independent variation, so the estimated combined spread is smaller than the total of all individual half-ranges.
Can a negative result indicate interference?
Yes, if the result is physically defined as clearance. Negative values mean overlap in the dimension-chain model, but contact stress and assembly feasibility require additional checks.
RSS and Worst Case Interpretation
A tolerance analysis calculator should reveal the controlling dimension, not just a final number. Use the contribution table to identify which tolerance may deserve inspection attention or a design change.
For stack up tolerance analysis, a numerical pass against requirement limits is only as reliable as the drawing dimensions, tolerance values, and completeness of the modeled chain. The RSS comparison is a preliminary statistical screen and is never a guarantee.
If production data are available, replace the simplified RSS assumption with actual means, standard deviations, covariance estimates and appropriate simulation or capability analysis.
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