Tolerance Stack‑Up Calculator

Worst‑Case analysis adds all tolerances linearly: WC = Σ|tᵢ|. It guarantees 100% assembly conformance because it accounts for every dimension being at its worst extreme simultaneously. RSS analysis sums the squares: RSS = √(Σtᵢ²). It predicts the range that 99.73% of assemblies will fall within (at 3σ), assuming normal distributions and independent dimensions. RSS typically gives a 30‑60% smaller total than WC, allowing looser and cheaper individual tolerances at the cost of a small non‑conformance risk.

Use Worst‑Case when 100% assembly conformance is required (safety‑critical parts, medical implants, aerospace flight controls), when the assembly has 4 or fewer dimensions, when you are producing one‑off prototypes, or when your process capability is unknown. This is the conservative approach to worst case tolerance analysis: assume every dimension hits its limit simultaneously and design for that worst case.

Include every dimension that affects the assembly gap or clearance you care about — typically 2 to 15 dimensions. A simple clearance (shaft in bore: 2 dimensions) needs minimal analysis. A bearing assembly (housing + two races + rolling elements + shaft + retaining ring: 5‑7 dimensions) benefits significantly from RSS. Complex gearboxes and engine assemblies can have 12+ dimensions. If you find yourself above 15 dimensions, you may be including dimensions that do not affect the specific gap you are analyzing — review your chain.

Cp (Process Capability) measures whether a process's spread (6σ) fits within the tolerance band. Cpk goes further — it measures whether the process is both tight enough AND centered on nominal. A process with Cp = 2.0 but Cpk = 0.8 is precisely consistent but consistently off‑target. For CNC machining, Cpk ≥ 1.33 is the standard for aerospace (AS9100) and medical devices. A tolerance stack up calculator that provides Cp/Cpk estimates helps you determine whether your tolerance scheme is realistic for the manufacturing processes you will use.

This tolerance stack up calculator handles linear ± tolerances. GD&T callouts — position tolerance, profile tolerance, runout, bonus tolerance at MMC/LMC — require specialized stack‑up methods that account for the geometric tolerance zone shape and datum reference frames. GD&T tolerance stack up analysis — using position zones, profile boundaries, and bonus tolerances — is more complex than linear stacks. For assemblies with GD&T, Baetro's engineering team reviews every drawing for free as part of our DFM process. Upload your CAD and we will verify the GD&T stack‑up before machining begins.

Standard CNC milling holds ±0.05‑0.10mm routinely. Precision CNC milling achieves ±0.01‑0.025mm with temperature control and high‑end tooling. CNC turning achieves tighter tolerances than milling — ±0.005‑0.01mm on precision lathes. Cylindrical grinding achieves ±0.002‑0.005mm. The tightest routinely achievable tolerance in production is around ±0.001mm using jig grinding, lapping, or honing — and each of these processes costs 5‑20× more than standard CNC machining. The process capability flags in this tolerance stack up calculator check every tolerance you enter against these real‑world limits.

A 100mm aluminum part grows by approximately 0.13mm when heated from 20°C to 80°C (ΔT = 60°C, CTE_aluminum ≈ 23 × 10⁻⁶/°C). If your assembly clearance from the stack‑up is 0.10mm, that thermal expansion consumes your entire clearance budget and the assembly will bind. Always calculate your stack‑up at both room temperature and maximum operating temperature. Use the Free Thermal Expansion Calculator to convert your stack‑up dimensions from 20°C to operating conditions.

For most CNC machined parts, ±0.05mm to ±0.10mm is the sweet spot — achievable by any competent shop without special processes or excessive inspection. ±0.025mm adds 50‑100% cost. ±0.01mm adds 100‑200% cost. ±0.005mm and tighter adds 200‑900% cost. The best strategy: use the contributor ranking in this tolerance stack up calculator to identify the one or two dimensions that drive the most variance, tighten those, and leave the rest at standard tolerances. That is how you get a capable assembly at minimum cost.