# Testing a Digital Scale

Dave Tutelman  -  December 1, 2005

There are times you will need to test a digital scale to see if it is working properly. It's easy to do if you have a set of calibrated weights of the proper mass just hanging around. Most of us don't. But you can still test its linearity and consistency, which is where it is most likely to show any defect.

## Equipment needed

• The digital scale to be tested, of course!
• Three weights, such that:
• They have the approximate weight ratio of 1 : 2 : 4.
• Their sum is a significant fraction (say 75% to 95%) of the capacity of the scale.
Here are some factors to consider when obtaining the weights:
• The exact ratio and sum is not important; just keep it approximately as described. The real goal is to be able to combine them for seven different weights, more or less evenly distributed over the range of the scale.
• For testing a digital scale of capacity around 20 pounds, I used three barbell weights of 10#, 5#, and 2-1/2# respectively. These are not their actual exact weights; one was a half-pound off, the others a third of a pound off. That is certainly close enough to be effective.
• Another approach, suggested by Ed Reeder, is water-filled plastic jugs (like milk containers). If you take a one-gallon, a half-gallon, and a quart jug and fill them completely, you will have about 15 pounds in total; that's enough to test a scale in the 20-pound range.
• If you are checking a digital scale whose range requires very low weights (say, less than 20 grams), then remember that coinage has fairly well-controlled weights. For instance, the US Nickel weighs 5.0 grams to within a tenth of a gram. (My thanks to Lee Beaumont for pointing this out.)
• Some way to place the three weights, alone or in combination, on the scale to be tested. This is generally easy if the scale is a platform scale; just place the weights on the platform. If it is a hanging scale (e.g.- a digital fishing scale with a hook), then you will need some sort of tray or bag. For the 20-pound capacity fishing scale, I found that a plastic grocery bag is strong enough to hold the weights, and the carry holes will fit over the hook. The bag weighs only 10 grams, which shows up as 0.02 pounds on the scale in question. If you are using milk jugs, loop a string through the handle and you can hang them from a hanging scale's hook. For some of the tests, you will need to figure the weight of the bag or string into the calculations.

## The tests

Below are several kinds of tests:
1. Zero tests, to see that the scale reads zero when it has no load on it.
2. Consistency tests, to see how repeatable the measurements are. If the scale doesn't give the same measurement when weighing the same object, from one try to the next, then it is not giving you a precision equal to its resolution..
3. Linearity tests, as a way of estimating the accuracy of the scale. The linearity tests determine whether weighing object A together with object B gives the sum of what each one weighs individually. If this works over the scale's range, then its accuracy can only be off by a constant factor.
4. Taring tests, to be sure that the linearity holds even where the readout is reset to zero at some nonzero weight.
In the tests that follow, we will call the three weights "A", "B", and "C" in order of increasing weight. For instance, the 2-1/2# weight will be called "A", the 5# weight will be called "B", and the 10# weight will be called "C".

### 1. Consistency and zero tests

Turn on the scale, with nothing on it to weigh. Don't even include the bag or tray -- absolutely nothing on it. The scale should read exactly zero. If it is more than one resolution unit off (e.g.- more than 1 gram for a scale with a resolution of 1 gram), then there is a zero error that should not be neglected.

Weigh A, B, and C separately. Cycle through A, B, and C in order, until you have weighed each one at least five times (and pick an odd number of times). The reason to cycle through them is to avoid any "cheater circuit" the scale may have. (Some digital instruments have the ability to recognize "the same input", and display it much faster than if they measured it completely. You don't want this ability to be exercised when you are testing precision.)

When you remove the load from the scale, see that it returns to zero. If it does not -- again, by more than one resolution unit -- it has a zero error.

Given those measurements, proceed for each of A, B, and C:
• Write down each measured weight. Write it as measured; do not subtract out the weight of any tray or bag you may use to hold the weight.
• Look at the results. The variation in the readings is the amount of inconsistency of the scale. (Well, it's the inconsistency of the scale plus your technique. Each scale takes certain handling to get accurate readings, and some are more fussy than others.)
• Write a single number that you will use for the weights of each of A, B, and C for the rest of the testing. Use the median of the measurements, not the average. The median is the number such that there are as many readings above and below that number. To do that, write down the numbers in sorted order. The middle number in the list is the median. For instance, suppose the readings were
[ 5.00, 5.02, 5.04, 5.04, 5.06 ]
then the middle reading, 5.04, is the median.
Record the median weights of A, B, and C, after subtracting out the weight of any tray or bag. Do not use the taring button to subtract out the weight of the tray. Instead, do the arithmetic explicitly to determine the weights by themselves. We will check the effectiveness of taring later; in the meantime, let's not do anything that depends on taring working correctly.

How big a consistency error is "acceptable"? That depends on your needs. However, I would be suspicious of the quality of any scale whose repeatability was worse than two units of resolution. (E.g.- readings that disagree by 3 or more grams for the 1-gram-resolution scale mentioned above.)

### 2. Linearity tests

To help you visualize the tests, a set of sample data follows this section. Refer to it as you read, to see what to expect. The linearity tests are the numbers in the second column.

Weigh the weights in combination, and write down their measured weights (after subtracting out the weight of the tray or bag). The combinations to be tested are:
• A + B
• A + C
• B + C
• A + B+ C
The final step is to do the arithmetic to see whether the scale is linear. For each combination, compare measured weight (the black numbers in the sample data table) with the sums of the weights (the red numbers). The discrepancy is a measure of how far the linearity is off. The scale represented by the sample data has very good linearity.

### 3. Taring tests

If your scale has a zero/tare button, now is the time to test that feature. The test will determine whether the linearity holds even when the readout is reset. (I know of no digital scale design where this should be a problem, but you ought to test it anyway; there may be designs out there that I don't know about.)

In the sample data, the taring tests are the third and fourth columns.

Go through each of the following tests. In each case, there is no need to do arithmetic; just use the tare button where directed. In each case, the measured weight should be the same as that of the weight we added after taring the scale. For instance, for the first test we add weight B after taring, so the measured weight should be the same as what we already know B to weigh.
• Put A on the tray. Press the tare/zero button. Add B and note the weight.
• Put B on the tray. Press the tare/zero button. Add A and note the weight.
• Put A on the tray. Press the tare/zero button. Add C and note the weight.
• Put C on the tray. Press the tare/zero button. Add A and note the weight.
• Put B on the tray. Press the tare/zero button. Add C and note the weight.
• Put C on the tray. Press the tare/zero button. Add B and note the weight.
If each of the noted weights is correct, then the taring feature operates across the range of the scale.

If this much works, you can be pretty sure the taring feature works fine. But if you want to be complete, you can also do the three-way taring tests (which are not shown in the sample data):
• Put A on the tray. Press the tare/zero button. Add B+C and note the weight.
• Put B on the tray. Press the tare/zero button. Add A+C and note the weight.
• Put C on the tray. Press the tare/zero button. Add A+B and note the weight.
• Put A+B on the tray. Press the tare/zero button. Add C and note the weight.
• Put A+C on the tray. Press the tare/zero button. Add B and note the weight.
• Put B+C on the tray. Press the tare/zero button. Add B and note the weight.

## Sample data

Here's the data from an actual test.

Scale: RiteWeight fishing scale
Max capacity = 18 pounds
Resolution = 0.02 pounds
Test weights (from weight lifting barbells)
A: Nominal 2.5 pounds
B: Nominal 5 pounds
C: Nominal 10 pounds

 Weights included Measured weight after subtraction Tare out lighter weight Tare out heavier weight A 2.34 B 5.20 C 9.44 A+B 7.56   (7.54) 5.20 2.32   (2.34) A+C 11.80   (11.78) 9.44 2.36   (2.34) B+C 14.64 9.44 5.18   (5.20) A+B+C 17.02   (16.98)

Numbers in red appear where there is a difference between the measured weight and what arithmetic says it should be. The red numbers are the "should be" numbers. Note that, of ten measurements:
• Four were exactly as expected.
• Five were off by only 0.02 pounds, the resolution of the scale. An error of one increment of resolution is never cause for alarm when testing the scale.
• Only one reading was off by more than the resolution; A+B+C was off by 0.04 pounds.
Conclusion: The linearity on this scale is very good.

## Notes on technique

I mentioned earlier that you are really measuring the combined errors of your scale and your skill in using it. There are little tricks of technique that scales will require to give good readings. They vary from scale to scale; you will have to learn by experience how to use yours, but here are a few common issues:
• Do not hold the scale in your hand when weighing something; you will not get consistent results that way. Put a platform scale on a stable surface, and hang a hanging scale from a stable hanging point. (I find shoelaces and two-by-fours to be very handy when using hanging scales.)
• The only thing the scale should touch is the surface on which it rests (or hangs from) and the object it is weighing. Similarly, the object being weighed should touch nothing but the scale. If this is violated, bad readings are likely to result.
• Continuing with the above advice, be sure that the scale's moving parts can move freely. For instance, the hanging hook on a digital scale should not touch the body of the scale, just the fitting that it hangs from.
• Learn to recognize when the scale has reached a stable reading.
• The "Tare/zero" button of a hanging scale will require a little practice to press it without momentarily loading or unloading the scale. Fortunately, you can tell whether you have pressed it correctly; if you did, it will settle quickly to a "0.000" reading. If it doesn't, then try again. Practice until you get it right most of the time.