How to Calculate % Study Variation

Updated 11 November 2026 · Standard formula, shown below

This guide explains how to calculate the percent study variation (%SV), a key metric in Gage Repeatability and Reproducibility (GR&R) studies. You’ll learn the step-by-step method to determine how much of your total measurement variation comes from the measurement system itself, helping you assess if your measurement process is adequate for your manufacturing or quality control needs.

What You’ll Need

Data from a GR&R study: typically 2-3 appraisers, 2-3 trials, and 5-10 parts.
A calculator or spreadsheet software (like Excel) for computations.
Basic understanding of standard deviation and variance.

Step-by-Step

Collect your data. Have each appraiser measure each part multiple times in a random order. Record all measurements in a table with rows for parts and columns for appraiser/trial combinations.
Calculate the average for each part across all appraisers and trials. For each part, sum all measurements and divide by the total number of measurements (appraisers × trials). This is the part average (\\(\\bar{x}_p\\)).
Calculate the overall average. Sum all part averages and divide by the number of parts. This is the grand average (\\(\\bar{x}\\)).
Calculate the repeatability (equipment variation, EV). For each appraiser, compute the range of their trials for each part. Then average these ranges across all parts for that appraiser. Average these appraiser ranges to get \\(\\bar{R}\\). Multiply by a constant \\(K_1\\) (from GR&R tables) based on number of trials: for 2 trials, \\(K_1 = 4.56\\); for 3 trials, \\(K_1 = 3.05\\). EV = \\(\\bar{R} \\times K_1\\).
Calculate the reproducibility (appraiser variation, AV). First, find the range of appraiser averages: \\(R_0 = \\max(\\bar{x}_a) – \\min(\\bar{x}_a)\\) where \\(\\bar{x}_a\\) is each appraiser’s average across all parts and trials. Then compute \\(AV = \\sqrt{(R_0 \\times K_2)^2 – (EV^2 / (n \\times r))}\\), where \\(K_2\\) is from tables (for 2 appraisers, \\(K_2 = 3.65\\); for 3, \\(K_2 = 2.70\\)), \\(n\\) is the number of parts, and \\(r\\) is the number of trials. If the value under the square root is negative, set AV = 0.
Calculate the measurement system variation (GRR). Combine EV and AV: \\(GRR = \\sqrt{EV^2 + AV^2}\\).
Calculate the part variation (PV). Find the range of part averages: \\(R_p = \\max(\\bar{x}_p) – \\min(\\bar{x}_p)\\). Then multiply by \\(K_3\\) (from tables, depending on number of parts; for 5 parts, \\(K_3 = 2.08\\); for 10 parts, \\(K_3 = 1.62\\)). PV = \\(R_p \\times K_3\\).
Calculate the total variation (TV). \\(TV = \\sqrt{GRR^2 + PV^2}\\).
Calculate %GRR and %SV. The percent study variation (%SV) is the same as %GRR in most contexts. Compute: \\(%SV = (GRR / TV) \\times 100\\). This is the percentage of total variation due to the measurement system. You can also compute %PV = (PV/TV) × 100.

Common Mistakes

Using the wrong K constants. These constants depend on the number of trials and appraisers. Always verify from a reliable GR&R table.
Mixing up EV and AV. EV is repeatability (variation within appraiser), AV is reproducibility (variation between appraisers). Ensure you’re using the correct ranges.
Forgetting to square or take square roots. The formulas involve squares and square roots; missing one step will give incorrect results.
Ignoring negative AV. If the calculation under the square root is negative, set AV to 0, not a negative number.

Tips

Use a spreadsheet to automate calculations and reduce errors.
Ensure your measurement units are consistent (e.g., all in millimeters or all in inches).
Randomize the order of measurements to avoid bias.
Interpret %SV: under 10% is generally acceptable, 10-30% is conditional, and over 30% is unacceptable.

Troubleshooting

If your %SV is over 30%, the measurement system needs improvement. Check for inadequate training, worn gauges, or poor gauge resolution.
If your AV is zero, it may mean appraisers are consistent, or that the calculation produced a negative under the square root (which is fine).
If your EV is very high, the gauge may have poor repeatability—try using a more precise instrument.
If you get a negative variance, double-check your ranges and constants; negative variance is not possible.

Frequently Asked Questions

What is the difference between %GRR and %SV?

In most GR&R studies, %SV (percent study variation) is the same as %GRR. It represents the percentage of total variation that comes from the measurement system. Some references use %SV to denote the contribution of the measurement system, while %GRR is specifically the combined repeatability and reproducibility. Practically, they are used interchangeably.

How many parts and appraisers do I need?

Typical GR&R studies use 10 parts, 3 appraisers, and 2-3 trials. However, for a quick study, you can use 5 parts and 2 appraisers. The more parts and trials, the more reliable the estimate.

Can I calculate %SV with only one appraiser?

Yes, but then you can only assess repeatability (EV), not reproducibility (AV). The %SV would be based on EV only, which is a partial assessment.

What is the acceptable %SV value?

Generally, %SV less than 10% is considered acceptable, 10% to 30% is conditional (depending on the application), and over 30% is unacceptable and requires improvement.

What if my measurement system has a bias or linearity problem?

%SV only assesses variation, not accuracy. Bias and linearity are separate studies. You should perform a bias and linearity study separately to ensure accuracy.

Can I use %SV for attribute gauges (go/no-go)?

No, %SV is for variable data (continuous measurements). For attribute data, use a different method like the Kappa study or Attribute Agreement Analysis.

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.