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Tolerance Stack-Up Calculator

Calculate worst-case and RSS (root sum square) tolerance stack-ups for multi-part assemblies. Add dimensions, set tolerances, and see how they accumulate in real time.

Quick Answer: How Do I Calculate a Tolerance Stack-Up?

A tolerance stack-up adds the individual part tolerances along a dimension chain to find the total assembly variation. Worst-case sums the absolute tolerances (WC = ∑|ti|) for the largest possible variation. RSS (root sum square) takes the square root of the summed squares (RSS = √∑ti²), giving a tighter, more realistic spread because all parts rarely hit their extremes at once.

This calculator computes worst-case and RSS stack-ups, plus Cp and Cpk capability estimates and per-contributor variance ranking. Inputs are the assembly spec tolerance and each dimension's nominal, tolerance (±) and direction (positive or negative).

Key facts: WC = ∑|ti| | RSS = √∑ti² | Cp = Spec / (6σ) | Cpk = min(USL−μ, μ−LSL) / 3σ | Cpk ≥ 1.33 is capable | typical chains run 3–10 dimensions | use worst-case for safety-critical parts, RSS for high-volume production.

Assembly Dimensions

Label Nominal Tolerance (±) Direction

Results

Total Nominal
0.0000
Worst-Case Analysis
WC Tolerance (±) 0.0000
WC Min 0.0000
WC Max 0.0000
RSS (Statistical) Analysis
RSS Tolerance (±) 0.0000
RSS Min 0.0000
RSS Max 0.0000
Capability Estimates
Cp (RSS-based) --
Cpk (RSS-based) --
Formulas:
WC = ∑|ti|  •  RSS = √∑ti²
Cp = Spec / (6σ)  •  Cpk = min(USL−μ, μ−LSL) / 3σ
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RSS assumes normal distribution (3σ). Verify critical assemblies with Monte Carlo simulation.

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Frequently Asked Questions

A tolerance stack-up is the cumulative effect of individual part tolerances in an assembly. When multiple parts fit together, each part's tolerance adds up. The total variation determines whether the assembly will function correctly or if parts may interfere or have excessive gaps.
Worst-case analysis assumes every dimension is at its maximum or minimum tolerance simultaneously. This gives the largest possible variation but is very conservative. RSS (root sum square) analysis uses statistics and assumes tolerances follow a normal distribution. RSS gives a more realistic estimate because it is unlikely all dimensions will be at their extremes at the same time.
Use worst-case analysis for safety-critical assemblies where every unit must function, such as aerospace and medical devices. Use RSS analysis for high-volume production where a small percentage of out-of-spec assemblies is acceptable and can be caught by inspection. RSS analysis typically results in looser individual tolerances, which reduces manufacturing cost.
Cp measures process capability by comparing the specification width to the process spread (6 sigma). A Cp of 1.0 means the process just fills the spec range. Cpk also accounts for how centered the process is within the spec. A Cpk of 1.33 or higher is generally considered capable. Higher values mean fewer defects.
Include every dimension in the tolerance chain that contributes to the critical assembly gap or fit. Start at a reference surface and trace a path through each part and gap to the feature you are analyzing. Each dimension along that path is one entry in the stack-up. Typically 3 to 10 dimensions are common, but complex assemblies can have more.

Fits & Tolerances Reference Series

Related references — jump to the one you need:

Press Fit CalculatorShrink Fit CalculatorFit CalculatorHole/Shaft ToleranceH7/g6 Fit ChartISO 2768 TolerancesBearing Fit ChartTolerance Stack-UpTolerance CostTolerance Guide

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