ISO standards and most of the standards labs around the world—NIST, the National Physical Laboratory, Physikalisch-Technische Bundesanstalt, etc. —provide definitions of these important words, and there are many contextual definitions that are specific to devices or situations. I’m not going to accurately match any of those definitions. I’ll just explain them as concepts with application examples.

First, it’s important to understand the differences in these words. Many people use them interchangeably, as if they have the same meaning. They don’t. Even if you know the definitions, there may be more to them than meets the eye. Let’s start with the definition of "accuracy."

Accurate to one apple
Take the Swiss story of William Tell and the apple on his son’s head. In 1307, he had to shoot an apple on his son’s head from 80 to 120 paces away (depending on which account you read) with his crossbow. You’re probably thinking this required him to be quite accurate, and you’re correct. However, all he had to do was hit the apple instead of his son’s head, or miss altogether. He had to be accurate to within one apple. Hitting the apple from 120 paces away required a precise shot. This makes accuracy and precision seem like the same thing.

In the context of this column, accuracy is how well a measurement matches or complies with a known standard. For example, if a reference gage block is 1.0002 in. long (leaving uncertainty for another column), and a measuring device reads out that gage block as 1.0002 in., the measuring device can be considered highly accurate.

William Tell’s requirement was to hit a target the size of the apple with an arrow at the required distance. If he didn’t have the necessary accuracy, he would have missed the apple, or worse. That makes it seem like his act required precision.

Precisely accurate?
One definition of precision is how well measurements match one another. In the Tell case, the precision and accuracy requirements were the same. He had to be precise enough to have “apple accuracy.” However, you can be precise but not very accurate.

Shooting at targets is a common way of explaining accuracy and precision. Instead of shooting the apple on someone’s head, imagine a dartboard with a bull’s-eye. Aiming at the bull’s-eye and hitting 6 in. to the right of it isn’t very accurate.

However, hitting that same point 6 in. to the right of the bull’s-eye more than once is precise. In other words, if William Tell shot more than one arrow, and they both were 6 inches to the right, that would be very precise, but inaccurate. Precision and accuracy can be equal, but they don’t need to be. Therefore, the words don’t have the same meaning.

Here’s another way of looking at it. Instead of individual shots at the target, let’s use a shotgun (Don’t try this at home). Pellets will hit all over the target. Overall, this isn’t very accurate, because most pellets will miss the bull’s eye. However, one or more pellets probably will hit the bull’s eye. So, is the shotgun accurate? The pellets that hit the target are accurate, but the shotgun approach isn’t very precise.

So what’s the resolution?
The William Tell example brings up another metrology word: resolution. Resolution is the smallest value or amount that can be measured. Although there’s no measuring in the apple-and-arrow example, there is a resolution aspect to it. Because the requirement was simply to hit the apple, not to hit it in a specific place, the measurement resolution was one apple. But hitting the apple with an arrow means that the resolution was the smaller size of the arrow. He had to hit the apple with arrow-sized resolution. This is analogous to using a measuring device with finer resolution than the measurement requirement of the object being measured.

Here’s another way of looking at resolution. Hitting the apple with an arrow requires different levels of precision as a function of distance. Hitting the apple with a crossbow from six feet is relatively easy (coarse resolution). Hitting that same apple from 100 paces away is a different matter (fine resolution). In other words, as long as the requirement is to hit the fixed-size apple, the farther away it gets, the greater the accuracy requirement.

Back to that gage block, an accurate measurement of it would match its certified length, but to what resolution? My example reported the length as 1.0002 in. If I’m calibrating this block, the measuring instrument should have resolution to another decimal place. If I have less resolution in my measuring device I might think I’m measuring accurately when I’m not.

On the other hand, it’s possible to go too far in the other direction, and to measure with too much resolution, like overspecifying a part. The resolution to which you measure the part is related to how accurately you want to know its size. In simplest terms, it means a spec of +/– 0.001 when +/– 0.01 might be good enough. Because it is possible to make or measure a part to extremely high resolution does not mean that it is necessary or cost-effective to do so.

Precisely accurate resolution
You can be precise, but inaccurate. You can be accurate and imprecise. You can be accurate and precise. You can have too much or too little resolution. Unless you know how these words are being used, be careful. You may be off-target.