# Tolerance Stack Calculator: Worst Case vs RSS

> Source: https://netray.co/tools/assembly-tolerance-stack-worst-case-vs-rss-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Add up the contributors in a linear stack and see the minimum gap by worst case, root-sum-square and a 1.5x modified RSS.

## Category

engineering-plm

## Industry

Automotive

## Audience

- Design engineer
- Quality engineer
- Supplier quality engineer

## Tool

**Kind:** calculator

**Inputs:**

#### Nominal gap or clearance

**Key:** gap

**Type:** number

**Default:** 0.7

**Step:** 0.01

**Unit:** mm

**Help:** Mean closing dimension when every part is at nominal.

#### Required minimum gap

**Key:** req

**Type:** number

**Default:** 0.25

**Step:** 0.01

**Unit:** mm

#### Contributor 1 tolerance (plus/minus)

**Key:** t1

**Type:** number

**Default:** 0.15

**Min:** 0

**Step:** 0.01

**Unit:** mm

#### Contributor 2 tolerance (plus/minus)

**Key:** t2

**Type:** number

**Default:** 0.1

**Min:** 0

**Step:** 0.01

**Unit:** mm

#### Contributor 3 tolerance (plus/minus)

**Key:** t3

**Type:** number

**Default:** 0.2

**Min:** 0

**Step:** 0.01

**Unit:** mm

#### Contributor 4 tolerance (plus/minus)

**Key:** t4

**Type:** number

**Default:** 0.08

**Min:** 0

**Step:** 0.01

**Unit:** mm

#### Contributor 5 tolerance (plus/minus)

**Key:** t5

**Type:** number

**Default:** 0.05

**Min:** 0

**Step:** 0.01

**Unit:** mm

**Outputs:**

#### Worst case tolerance (sum)

**Key:** wc

**Expr:** t1 + t2 + t3 + t4 + t5

**Format:** decimal

#### RSS tolerance

**Key:** rss

**Expr:** sqrt(t1 * t1 + t2 * t2 + t3 * t3 + t4 * t4 + t5 * t5)

**Format:** decimal

#### Minimum gap, worst case

**Key:** wc_min

**Expr:** gap - wc

**Format:** decimal

**Primary:** true

**Description:** Guaranteed if every part is within tolerance.

#### Minimum gap, RSS

**Key:** rss_min

**Expr:** gap - rss

**Format:** decimal

**Primary:** true

**Description:** Statistical, assumes independent centered normal contributors.

#### Minimum gap, modified RSS (1.5x)

**Key:** bender_min

**Expr:** gap - 1.5 * rss

**Format:** decimal

**Description:** Conservative allowance for mean shifts and non-normality.

#### Margin to requirement, worst case

**Key:** m_wc

**Expr:** wc_min - req

**Format:** decimal

#### Margin to requirement, RSS

**Key:** m_rss

**Expr:** rss_min - req

**Format:** decimal

**Chart:**

#### Minimum gap vs contributor 3 tolerance

**Type:** line

**X:** t3

**From:** 0.02

**To:** 0.4

**Steps:** 20

**Series:**

- wc_min
- bender_min
- rss_min

**Disclaimer:** One-dimensional, linear stack with symmetric tolerances. Does not cover geometric tolerance bonus, 3D effects, thermal growth or assembly shift.

## Content

**Intro:** Tolerance stacks decide whether parts assemble, and the method you pick decides how much tolerance each part gets. This calculator compares worst case, statistical RSS and modified RSS for a five-contributor linear stack so you can see the gap you can promise and what each method costs in tolerance.

**Sections:**

#### How to use it

**Body:** Express the closing gap as a nominal and list each contributor's plus or minus tolerance in the same unit, with all contributors working in a consistent direction. Enter the minimum gap needed for assembly or function. The tool returns the minimum gap by each method and the margin to your requirement. Sweep a contributor's tolerance in the chart to see how much you could relax it, or must tighten it, before margin disappears.

#### Worst case, RSS and modified RSS

**Body:** Worst case adds all tolerances, guaranteeing assembly even when every part is at its limit, but it drives tight, costly tolerances. RSS takes the square root of the sum of squares, assuming independent, centered, normal contributions, and gives a much smaller total. Modified RSS multiplies the RSS value by a factor, commonly 1.5, to allow for mean shifts and non-normal distributions. The right choice depends on risk, process capability and whether the parts are 100 percent inspected.

#### Linking to capability

**Body:** RSS is only legitimate if each contributor's process is capable and centered. If a supplier's Ppk is marginal or a feature is bimodal because of two cavities, statistical stacking overstates your margin. This is why stack analyses and PPAP capability data belong together: the study tells you whether the assumptions behind the stack are true. Where capability is unproven, use worst case or modified RSS and plan 100 percent checks on the key contributor.

#### Common mistakes

**Body:** Mixing bilateral and unilateral tolerances without converting them to a mean and a plus or minus value is the most common mistake. Others include ignoring geometric tolerances that shift position, forgetting the direction of each dimension in the loop, and applying RSS with only two or three contributors, where the benefit over worst case is small and the normality assumption matters more.

**Cta:** If your drawings and tolerances live in PLM or ERP records, Netray can help connect them to measured results so stack assumptions are checked against real data.

**Faq:**

#### When is worst case the right method?

**Answer:** Use worst case for safety-critical fits, few contributors, low-volume parts, or when the process capability is unknown. It guarantees assembly but may force tighter and more expensive tolerances.

#### Why is the factor 1.5 used?

**Answer:** A multiplier of about 1.5 on the RSS result is a common empirical allowance for mean shift and non-normal distributions. It is a rule of thumb, not a theorem, so agree on it with your design authority.

#### Can I use RSS with inspected parts?

**Answer:** Inspected and sorted parts are often truncated, not normal, so RSS can be optimistic or pessimistic depending on the sort. Treat the result with caution and validate with measured assemblies.

#### Does this handle GD&T?

**Answer:** No. It handles linear dimensions with plus or minus tolerances. Position, profile and datum shift need a full GD&T stack method or software.

## Search terms

tolerance stack up calculator, worst case vs rss tolerance, rss tolerance stack, one dimensional tolerance stack, tolerance stack gap calculator, modified rss bender, stack up analysis excel, dimensional tolerance analysis

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