Basics of Metrology : Measurement Uncertainty and Accuracy of Equipment

If you’ve ever contracted 3D Engineering Solutions to perform a part inspection for you then you’ve more than likely received a certified inspection report. There are a lot of items on this report, but aside from the results you are looking for, one of the more important items will be the stated measurement uncertainty for the equipment we used.

What does the measurement uncertainty statement mean to you as a customer of 3D Engineering Solutions?

In the science of measurement, or metrology, engineers typically depend on measurement tools that are very accurate, but how does this stated equipment accuracy translate to real world measurements that can be trusted?

Accuracy is used by the manufacturers of our equipment, whether it’s a dial caliper or a laser scanner, to tell us the degree to which a measurement conforms to somestandard. Normally the manufacturer will supply a certificate stating that they have checked the equipment to a calibration standard that has traceability to NIST (National Institute of Standards and Technology) or other governing body.

Per the NIST website, stating that a standard is traceable to NIST means that it holds the “property of a measurement result whereby the result can be related to a reference through a documented unbroken chain of calibrations” (Technology, NIST Traceability Policy – External, 2014)  This means  you can, should you ever be required to, follow the paper trail from our equipment back to the source standard at NIST.  This is all well and good and provides us an excellent starting point, but what about the effects of all of the other factors such as the individual using the equipment and their level of training? What about the environment in which the equipment is being used? Is the temperature and humidity stable? How do we evaluate and state the full uncertainty in measurement and what does that statement mean to you as a customer of 3D Engineering Solutions?

Let us first explain the factors commonly used to evaluate this. We’ll use our 24 inch Mitutoyo height gage as an example, since most people are familiar with this type of measurement equipment. The first item we look at is the resolution of the gage. We find the resolution of the gage stated by the manufacturer as .00005 inch (Mitutoyo). The manufacturers stated accuracy for this is +2.5 micrometers at 1 inch so we’ll record this as the accuracy.Note that Mitutoyo uses a linear equation formula, similar to what we will use for our uncertainty, so it depends on the measured dimension (Mitutoyo). Since 3DES has a third party calibrate our metrology tools on regular intervals, we also need to review the measurement uncertainty of the calibration and include this number. At that point we look at the deviation between multiple measurements for single or multiple users. For the height gage we would use a registered standard such as a calibrated gage block, and then have one or more users take a single measurement multiple times. From this data we glean the repeatability of personnel. With all of this data we can then come up with the Expanded Measurement Uncertainty for our height gage. In this case the Expanded Uncertainty is 6+0.1L micrometers, where L = measured length in meters. There is quite a bit more going on here, but for brevity we have only covered the basic ideas. If you want to learn more you can read the NIST Technical Note 1297 which covers the guidelines for evaluating and expressing the uncertainty of NIST measurement results. (NIST)

Now that we’ve gone through thebasics of how we obtain the uncertainty numbers, let’s take a look at what these numbers mean to you for the purposes of reading a certified inspection report.

Let’s say you send in a widget and you want 3DES to verify dimension x1 on 50 pcs. Dimension x1 has an overall tolerance of +.001 inch according to the widget manufacturing drawing you’ve supplied along with the part. We know that we need something that is at least as good as +.0001-.0002 inch, as this will place our uncertainty of measurement at around 10% – 20% of your total allowable tolerance. Now let’s say that dimension x1 = 2.250 inches.  We can now use the formula above to verify that the height gage is an acceptable method of measuring your part.


The above looks scary, but what it is telling us is that 3D Engineering Solutions can use our 24 inch digital height gage to measure a distance of 2.250 inches, with a confidence level of 95%, to within plus or minus two ten-thousandths of an inch. Note that any dimension that takes our uncertainty up past 20% is eating into your tolerance band, but the .0000364 inch remaining in our calculation should be negligible for what we are doing here. I’d say that our height gage would be the ideal measurement tool for this wouldn’t you!

If you would like to know more about the equipment available at 3D Engineering Solutions or which method is best suited for your requirements you can contact 3D Engineering Solutions at 513-771-7710 or use our contact form at

Works Cited

Mitutoyo. (n.d.). Product Information. Retrieved from QM-Height Series 518-High Precision ABSOLUTE Digital Height Gage – See more at:

NIST. (n.d.). NIST Physical Measurement Laboratory . Retrieved from NIST Technical Note 1297:

Technology, T. N. (2014, May 14). NIST Traceability Policy – External. Retrieved December 16, 2015, from NIST:

Technology, T. N. (2015, August). Constants, Units and Uncertainty. Retrieved December 16, 2015, from NIST Reference on Constants, Units, and Uncertainty: