Gage R&R Summary Calculator (% study variation)

Understanding the gage R&R calculator — concept and principle

A gage repeatability and reproducibility (R&R) study asks whether a measurement system is good enough to tell parts apart. From the standard deviations for repeatability (EV), reproducibility (AV) and part-to-part variation (PV) (usually from a crossed study of several operators measuring the same parts repeatedly) the calculator gives the %GRR of total variation, the number of distinct categories (ndc) and a verdict based on the AIAG guideline.

EV and AV combine like the sides of a right triangle; the gauge spread is then compared with the part spread.

How it is calculated

GRR = √(EV² + AV²): combined measurement-system variation.
TV = √(GRR² + PV²): total observed variation.
%GRR = GRR ÷ TV × 100.
ndc = 1.41 × PV ÷ GRR, rounded down to a whole number.

Verdict: below 10% acceptable, 10–30% marginal, above 30% unacceptable. All three inputs must be in the same measurement unit.

The principle

Independent sources of variation add as variances, not as standard deviations. What you observe on a measured part is the true part difference plus the scatter of the gauge itself (EV, same operator, same part, repeated) plus the differences between operators (AV). That is why each step uses a square root of a sum of squares. %GRR compares the measurement noise with the total spread. The ndc estimates how many non-overlapping groups the gauge can reliably separate within the part variation; 1.41 is √2.

Worked example

Inputs: EV = 0.02, AV = 0.015, PV = 0.12.
GRR = √(0.02² + 0.015²) = √0.000625 = 0.025.
TV = √(0.025² + 0.12²) = √0.015025 = 0.12258.
%GRR = 0.025 ÷ 0.12258 × 100 = 20.4% → marginal (10–30%).
ndc = 1.41 × 0.12 ÷ 0.025 = 6.77 → 6.

Each point is the calculator re-run with only “Part-to-part σ (PV)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Part-to-part σ (PV)	%GRR
0.03	64.02%
0.06	38.46%
0.09	26.76%
0.12	20.4%
0.15	16.44%
0.18	13.76%
0.24	10.36%

How to read the result

Where does your result fall?

At 20.4% the gauge may be acceptable depending on how important the characteristic is, the cost of a better gauge and the cost of repairs; the AIAG manual leaves this to the customer and the application. An ndc of 5 or more is the usual minimum. If repeatability (EV) dominates, look at the instrument, fixturing or method; if reproducibility (AV) dominates, look at operator training and clear procedures.

Common mistakes

Adding percentages: %EV + %AV does not equal %GRR, because variances, not percentages, add.
Choosing study parts that cover a narrow range, which makes PV small and %GRR look worse than in production.
Comparing GRR with total variation when the real question is conformance to a tolerance; then %GRR of tolerance (6 × GRR ÷ tolerance) is the relevant figure.

Keep in mind: The result is only as good as the study behind it: parts should represent the process range, operators should measure in random order without knowing earlier readings, and the gauge should be stable over time. Check the customer's own acceptance rules before approving a system.

Frequently asked questions

Why does the verdict use 10% and 30%?

These are the guidelines in the AIAG MSA reference manual for percentage of total variation; they are not physical limits.

Can I enter 6σ spreads instead of σ?

Yes, as long as all three are on the same basis. Ratios and ndc are unchanged when every value is scaled by the same factor.

Sources: AIAG, Measurement Systems Analysis (MSA) Reference Manual, 4th edition (2010) · D. C. Montgomery, Introduction to Statistical Quality Control, Wiley

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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