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RESOLUTION,PRECISION, AND ACCURACYMaria PapadakisISATJames Madison University

There are three basic concepts related to instrumentation and measurement that people often

confuse, largely because of differences in our common use of the words precision and accuracy

and the professional meanings of these terms. We want to make sure that you clearly understandthese three conceptsresolution, precision, and accuracyand know how they are correctly

used in science and engineering.

RESOLUTION AND PRECISION

Very simply, resolution is the smallest increment of a unit that an instrument can detect or

measure. For example, a ruler that has millimeters marked on it has a resolution of 1 mm, or

1/1000 of a meter; a car odometer has a resolution of 1/10 mile. Another way of saying this is that

resolution is the smallest interval that an instrument can measure. Often, but not always,

resolution is indicated by the scale or readout of the instrumentthe smallest tick mark on the

scale or the last decimal place in the case of digital instruments. Resolution matters because itdictates the number of significant digits we can show in a measure, and hence determines the

precision of any single measurement or observation (which is notthe same thing as the precision

of the instrument that we use). Obviously, the smaller the division of our measurement scales,

the more precise our measurements will be.

There are two basic principles about resolution and its relationship to measurement precision

that you need to know, understand, and apply as you work with instrumentation. First, the

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smaller the intervals on our scale, the more precise our measurements will be: the precision

of our measurements is created by the resolution of the instrument that we are working

with.

Refined scales and high instrument resolutions lead to more precise measurements because

they allow us to be more consistently specific in our measurements. Consider the pencil in the

two images below. The top scale has a lower resolution than the bottom: it measures only to thewhole centimeter, as opposed to millimeters. In trying to read the top scale, we could say that the

pencil measures about9.5 cm. We have to eyeball the increment between 9 and 10 since it isnot marked for us. (In fact, the top ruler has an impliedresolution of 0.5 cm, since most people

can visually divide the distance between those tick marks in half.) However, such eyeballing

leads to errors, since not everyone would estimate the interval between 9 and 10 the same: some

people might see this pencil as 9.6 cm, others perhaps 9.4 cm. This is known as a parallax

effectthe differences in visual perception that people have when evaluating distances between

points.

In contrast, the bottom ruler, with a higher resolution, will lead very consistently to observed

readings of 9.5 cm for the length of this pencil, regardless of who is making the measurement or

how many times this particular pencil is measured. Such consistency when measurements are

repeated reflects theprecision of the instrument itselfhow well it can consistently produce the

exact same measurement for the exact same item over and over again. This is why resolution and

precision are so intimately related. As resolution increases, it increases the likelihood that an

instrument will yield the same reading for the same object when measured multiple times. This is

what is meant by the

concept ofprecision.

Nonetheless, it is not

possible to measure this

pencil exactly. Consider

the line at right. It looks

like it is 9.6 cm. But what if we could magnify this image? As seen below, the line may actually

be a little longer than 9.6 cm, but how do we decide exactly where the line ends? And is the

absolute end of the line really the best place to take this measurement? In addition, perhaps the

Source of images: http://www.wcsscience.com/precision/andaccuracy.html [Aug. 20, 2003].

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ruler itself isnt accuratethe

tick marks might not be

correctly located at the exact

millimeter positions.

As these images illustrate,

our measurements are limitedby the resolution of the

instrument itself. As a

consequence, it is essential to

apply principle number two:

Report measurements only in

the number of significant

digits that reflect the

resolution of the instrument

from which they were

obtained.

In the case of our line, its

length is correctly reported as9.6 cm, not 9.60 or 9.600 cm.

Even though 9.6, 9.60, and

9.600 are all the same numbers,

they are not the same

measurements. Numbers are

absolute, but measurements

always have varying degrees of

precision that we signal with the

proper use of significant digits. Since the resolution of the ruler is only to 1/10 of a centimeter,

you can only report the length to one decimal place. If you reported that the length was 9.60, it

implies that you could visually distinguish and measure intervals of 1/100 with this ruler, and that

you in fact did measure the line to that degree of precision. This would be false and incorrect.

Another example is useful. Suppose you need to optimize the number of blanks that can be

stamped out of a sheet of metal. You measure its length and width as 8.69 cm by 10.54 cm. This

leads to an area of 91.5926 cm2 when calculated purely mathematically. However, if we

acknowledge the inherent uncertainty of the original measurements as reflected by their

significant digits, the area of the piece of metal is correctly reported as 91.59 cm2.

ACCURACY

Accuracy represents how close a measurement is to the true value of the property that is being

measured. Measurements can be highly precise, but not true. The easiest was to think about this iswith a digital bathroom scale. You can weigh yourself on one of these scales to 1/100th of a

pound, and it may tell you the same weight exactly over and over again. But the scale itself can

be off, a few pounds light or heavy, for example. You can therefore get a measure of your weight

very consistently and very preciselyto within 1/100 poundsbut it may not be your true

weight. The scale is not accurate, but it is precise.

Source of images:http://www.carlton.paschools.pa.sk.ca/chemical/Sigfigs/recording_results.htm Au ust 21 2003 .