Tolerance Stack-Up Calculator

Formula

• Nominal gap = Σ signed component nominals
• WC min gap = nominal − Σ minus tolerances
• WC max gap = nominal + Σ plus tolerances
• RSS tolerance = σ × √(Σ (Ti/2)²)

About this calculator

Part of our Fixture & Tooling Calculators collection. Clamping, locating pins, tolerance stack-up, and gauge R&R.

How it works

Nominal gap is the signed sum of loop dimensions. Worst-case limits add all tolerances in the direction that closes or opens the gap. RSS uses statistical tolerance combination at your chosen sigma level. Compare both methods to your required min and max gap.

Enter your values in the inputs above and click CALCULATE. Results appear on the right without a page reload. No login and no server upload.

Worked example

Four-component loop with default fixture stack values and σ = 3.

1. Nominal gap = 50 − 49.6 − 0.2 − 0.1 = 0.10 mm
2. WC range = 0.10 ± 0.12 → −0.02 to 0.22 mm
3. RSS 3σ tolerance ≈ 0.203 mm

Result: Worst-case and RSS both fail a 0 to 1 mm requirement on defaults.

When to use

• Checking assembly gap or interference in a dimension loop
• Comparing worst-case vs statistical tolerance methods
• Fixture and housing stack-up before detailed GD&T

Limitations

• Fixed four-component loop; not a general N-dimension stacker
• RSS assumes normal distribution and independent tolerances
• Does not apply geometric tolerances or bonus tolerance

FAQ

Worst-case vs RSS?

Worst-case adds all tolerances in the closing direction and is conservative. RSS combines tolerances statistically and is typical for mass production with controlled processes.

What sigma level should I use?

3σ is common for RSS stack-up (≈99.7% of assemblies). Use 4σ or 5σ for tighter risk control.