F-01
Total nominal stack
Σ(direction_i × n_i)
Adds + rows, subtracts - rows.
Engineering calculator
Tolerance Stackup Analysis
Define a 1D stack, edit tolerances inline, and validate worst-case and RSS behavior against engineering reference cases.
F-01 / F-02 / F-03V-01 to V-05Units: mm
Stack definition
Edit rows inline. Calculation output will update from this state.
Stack equation
Live signed nominal contribution by row.
35.00 mm
1+10.002+20.003+5.00
Contribution is the signed nominal term used in the equation. Tolerance propagation is shown separately in the results panel.
| # | Label | Nominal (mm) | Upper Tol | Lower Tol | Direction | Contribution | Delete |
|---|---|---|---|---|---|---|---|
| 1 | +10.00 | ||||||
| 2 | +20.00 | ||||||
| 3 | +5.00 |
Monte Carlo
Distribution estimate
Normal sampling with σ ≈ tolerance / 3, clipped to each row tolerance bounds.
Mean
34.9991
Range
34.7266 to 35.2331
P05
34.8703
P95
35.1231
Histogram
2000 samples
34.7266
3
34.7688
9
34.8110
44
34.8532
128
34.8954
230
34.9376
365
34.9798
452
35.0221
375
35.0643
239
35.1065
116
35.1487
31
35.1909
8
Results
F-01 total nominal, F-02 worst-case, and F-03 RSS approximation.
Total nominal
35.0000
Worst-case min
34.6500
Worst-case max
35.3500
RSS tolerance
0.2291
RSS min
34.7709
RSS max
35.2291
RSS is shown as an approximation. Worst-case is deterministic and conservative.
Output is formatted for engineering review: nominal values are exact, worst-case is conservative, and RSS is a statistical estimate.
Formula reference
How the stack is calculated
F-02
Worst-case bounds
local_min = n_i - t_minus_i, local_max = n_i + t_plus_i
+ rows use local bounds directly.
F-03
RSS approximation
RSS_tol = sqrt(Σ(((t_plus_i + t_minus_i)/2)^2))
Approximation band, not worst-case.
Assumptions
Modeling notes
1D linear chain onlyRSS assumes independenceAsymmetric tolerances supportedMonte Carlo is an estimate
Validation cases
V-01 All positiveV-02 Mixed directionsV-03 Asymmetric tolerancesV-04 Zero toleranceV-05 Invalid input
Current stack expression
Live signed nominal terms
+10.00 + +20.00 + +5.00
Same signed nominal expression used by the calculator.