# Gage R&R NDC and Percent Tolerance Calculator

> Source: https://netray.co/tools/gage-rr-ndc-and-percent-tolerance-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Convert part-to-part and gage R&R standard deviations into NDC, %GRR of study variation and %GRR of tolerance, and see how NDC falls as gage error grows.

## Category

quality

## Industry

Precision Manufacturing

## Audience

- Quality engineer
- Metrologist
- Supplier quality

## Tool

**Kind:** calculator

**Inputs:**

#### Part-to-part standard deviation

**Key:** pv_sd

**Type:** number

**Default:** 0.012

**Min:** 0

**Step:** 0.001

**Unit:** mm

**Help:** Sigma of part variation (PV) from your ANOVA or average-and-range study.

#### Gage R&R standard deviation

**Key:** grr_sd

**Type:** number

**Default:** 0.0024

**Min:** 0

**Step:** 0.0001

**Unit:** mm

**Help:** Combined repeatability and reproducibility sigma.

#### Total tolerance (USL minus LSL)

**Key:** tol

**Type:** number

**Default:** 0.1

**Min:** 0

**Step:** 0.01

**Unit:** mm

**Help:** Full width of the specification.

#### Study spread multiple

**Key:** spread

**Type:** select

**Default:** 6

**Options:**

##### 6 sigma (99.73%)

**Value:** 6

##### 5.15 sigma (99%)

**Value:** 5.15

**Outputs:**

#### Total variation sigma

**Key:** tv_sd

**Expr:** sqrt(pv_sd * pv_sd + grr_sd * grr_sd)

**Format:** decimal

**Description:** Part variation and gage variation combined in quadrature.

#### %GRR of study variation

**Key:** pct_sv

**Expr:** grr_sd / tv_sd * 100

**Format:** percent

**Primary:** true

**Description:** Under 10% is generally acceptable, 10 to 30% marginal, over 30% unacceptable.

#### %GRR of tolerance

**Key:** pct_tol

**Expr:** spread * grr_sd / tol * 100

**Format:** percent

**Primary:** true

**Description:** Gage spread as a share of the specification width.

#### Number of distinct categories

**Key:** ndc

**Expr:** floor(1.41 * pv_sd / grr_sd)

**Format:** integer

**Description:** AIAG guidance asks for 5 or more.

#### %GRR of variance

**Key:** pct_var

**Expr:** grr_sd * grr_sd / (tv_sd * tv_sd) * 100

**Format:** percent

**Description:** Contribution ratio, the square of the study variation ratio.

**Chart:**

#### %GRR of tolerance and NDC as gage sigma grows

**Type:** line

**X:** grr_sd

**From:** 0.0005

**To:** 0.01

**Steps:** 30

**Series:**

- pct_tol
- ndc

**Disclaimer:** Planning aid based on the AIAG MSA reference manual formulas. Use your own study software for formal reports and follow your customer's acceptance rules.

## Content

**Intro:** A gage R&R study gives you sigma values, and the decision comes from three ratios: percent of study variation, percent of tolerance and the number of distinct categories. This calculator computes all three from the sigmas you already have and shows how fast they degrade when gage error grows.

**Sections:**

#### How to use the calculator

**Body:** Enter the part-to-part standard deviation and the gage R&R standard deviation from your study output, then the tolerance width. Choose the 6 sigma spread used by current AIAG practice, or 5.15 sigma if your customer still uses the older 99 percent convention. The primary results are %GRR of study variation and %GRR of tolerance. The chart sweeps gage sigma so you can see how much improvement a better fixture or a finer-resolution gage would buy before you spend money.

**Bullets:**

- Use sigma, not the 5.15 or 6 sigma spread, as the input.
- Part variation must come from parts that represent the real process range.
- Keep units consistent between sigma and tolerance.

#### The formulas behind it

**Body:** Total variation is the square root of the sum of squares of part variation and gage R&R. Percent study variation is gage sigma divided by total sigma. Percent tolerance is the chosen spread multiple times gage sigma divided by the tolerance width. The number of distinct categories is 1.41 times part sigma over gage sigma, truncated to an integer. Because variances add and not standard deviations, a gage that looks acceptable on study variation can still consume a large part of a tight tolerance.

#### Reading the result

**Body:** Under 10 percent of study variation is generally acceptable, 10 to 30 percent may be accepted depending on cost and risk, and over 30 percent needs improvement. NDC of 5 or more means the gage can reliably sort parts into at least five groups. A low %GRR of study variation with a high %GRR of tolerance usually means your parts vary far more than the specification allows, which is a process issue, not a gage issue. Judge the gage against the purpose: process control cares about study variation, part acceptance cares about tolerance.

#### Common mistakes

**Body:** The most common error is a study with parts clustered near nominal. That shrinks part variation, so %GRR of study variation looks poor even when the gage is fine. The opposite error is picking parts across a range wider than the process ever produces, which flatters the gage. Also avoid mixing a 5.15 sigma study report with a 6 sigma tolerance rule. Record which convention the source report used before comparing results across suppliers.

**Cta:** If your gage studies live in spreadsheets and your ERP quality module never sees them, we can help connect study results to inspection plans and supplier records.

**Faq:**

#### What is an acceptable NDC?

**Answer:** AIAG MSA guidance treats an NDC of 5 or more as acceptable for process analysis. Values of 1 mean the gage cannot tell parts apart, and 2 to 4 only allow coarse sorting such as pass or fail with limited information.

#### Why is %GRR of tolerance different from %GRR of study variation?

**Answer:** Study variation compares gage error to the variation actually seen in the parts. Tolerance compares it to the specification width. If the process is much tighter or wider than the tolerance, the two numbers diverge.

#### Which spread multiple should I pick?

**Answer:** Use 6 sigma unless your customer or older procedure specifies 5.15. Current AIAG practice uses 6, and mixing conventions between studies makes comparison unreliable.

#### Can I enter variance instead of sigma?

**Answer:** Take the square root of each variance component first. The calculator expects standard deviations. Entering variance would give wrong ratios.

## Search terms

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