All measurements are estimates

A 3½-digit multimeter has a display range of 0 to ±19.99 V on the 20-V scale. Courtesy of B+K Precision.

Whenever you make a measurement, the result you get is an estimate of the true value. Instrument makers publish accuracy specifications, usually expressed as a percent—but a percent of what? Through the accuracy specification, the manufacturer guarantees that a measurement is within some tolerance of the actual reading. Therefore, accuracy really indicates the measurement uncertainty.

Here’s an example using a B&K Precision Model 2707A handheld multimeter. Assume you want to measure around 10 V. The B&K 2707A has a 2000-count display, meaning that it has a range of 0 to ±1999. To measure 10 V with the meter’s finest resolution, set the dial to 20 VDC. The measurement range is 0 V to ±19.99 V. Now, assume you make a measurement and get a reading of 10.00 VDC. What’s the uncertainty of the measurement?

B&K specifies the meter’s DC accuracy at “±0.5% plus 1 digit,” but is that ±0.5% of reading or of full scale? Unless the manufacturer specifies a percentage of reading, you must assume the uncertainty is a percentage of full scale. So, 0.5% of 20 V is 0.1 V.

Then, you must add one digit (sometimes called a count), which is 0.01 V (10 mV) on the 20-V range. Thus, the uncertainty of your measurement is ±0.11 V. A 10.00 reading, assuming that the meter is perfectly in calibration, means that the true value can range from 9.89 V to 10.11 V.

There’s a lot more to measurement uncertainty, a topic that would take many pages to cover thoroughly. For example, it’s still possible to get a measurement reading that is outside the uncertainty range even when the actual value is within the range. Every measurement, therefore, has an associated uncertainty and a confidence level. When you have an instrument calibrated, you can request an uncertainty specification and a confidence level that your measurements will be within the manufacturer’s specifications. Remember that instruments drift over time, which increases uncertainty and decreases confidence.