For several years, there has been an increase in the use of Class II scales in commercial applications. Previously relegated to pharmacies, jewelry stores, and facilities that receive or process grain (e.g., a grain elevator or feed mill), these scales are now found in retail environments where high-priced commodities are sold. While the cost of these commodities warrants the use of a Class II scale, several things must be considered when selecting and evaluating these devices.
Before going any further, it is important to be familiar with the definition of certain terms, especially how e and d are defined, to understand the requirements that apply to Class II devices and facilitate the proper selection of this type of device. These terms are found in NIST Handbook 44 (NIST HB 44), Appendix D. Definitions:
$$n = \frac{Capacity}{e}$$
To restate the definitions of e and d:
See Figure below for an illustration of e and d divisions.
To ensure equitable transactions, a commercial device must be suitable for the application in which it is used. NIST HB 44, Section 2.20. Scales includes criteria to consider when selecting a scale to determine if it is suitable for a particular application:
NIST HB 44 UR.1. Selection Requirements. – Equipment shall be suitable for the service in which it is used with respect to elements of its design, including but not limited to, its capacity, number of scale divisions, value of the scale division or verification scale division, minimum capacity, and computing capability.
This paragraph, including its sub-paragraphs and tables, deals with suitability. While what is considered suitable for each application is not always explicitly defined in this section of the handbook, it must be considered for each application. Some factors to be considered include:
Some of these requirements are fairly straightforward, while others are a little more complicated. The information in the following example will be used to evaluate these factors to determine parameters for an appropriate scale:
A retailer of fine herbs, spices, and seasonings has decided to sell some of these items from bulk. The most expensive item is Persian Saffron, which is sold for $ 4.20 per gram (g), and the least costly is Tellicherry Peppercorns, which is sold for $ 0.12/g. The retailer expects to sell the saffron in 1 g – 2 g increments and the pepper in 100 g – 200 g increments.
The retailer also does not expect to sell more than 1 lb (454 g) of any bulk item. The items will be weighed in a “scoop” (≈ 340 g) similar to the bowl pictured here to determine the net weight, which will then be transferred to a container such as a jar for the customer to take with them. The retailer indicates that the current Point-of-Sale program can be interfaced with a scale.
Capacity. UR.3.2. Maximum Load specifies that a scale cannot be used to weigh loads more than the nominal capacity of that scale. A scale with an 820 g capacity should be suitable for weighing these items in a scoop.
Number of scale divisions/value of the scale division or verification scale division/minimum capacity. These are interrelated. Per the above definition, the number of scale divisions (n) is always the number of verification scale divisions. Per Table 3. Parameters for Accuracy Classes, depending on the value of the verification scale division (e), a Class II scale must either have a minimum of 100 e (e from 1 to 50 mg) or 5000 e (e ≥ 100 mg). The maximum number of verification scale divisions is 100,000 e. We’ve determined an acceptable capacity of 820 g. To determine the smallest e allowed on this scale the capacity of 820 g is divided by the maximum number of scale divisions (n):
$$\frac{820 g}{100000}=0.0082 g$$
An e of 0.0082 g is not possible Per S.1.2. Value of Scale Division Units. This includes the verification scale division, which must be equal to 1, 2, or 5, or a decimal multiple or submultiple of 1, 2, or 5. In this case, an e of 0.005 g would result in a scale with 124,000 e, exceeding the parameters specified in Table 3. The smallest e possible on this scale is 0.01 g which would result in an n = 82,000. The largest e possible is 0.1 g, an n = 8,200 e, just above the minimum required by Table 3. The table below displays the range of possible verification scale divisions (e) based on a capacity of 820 g. The values of e that are compatible with a capacity of 820 g are inside the box in the table.
Verification Scale Division | Capacity | Table 3 Minimum n | Table 3 Maximum n | |
---|---|---|---|---|
0.005 g | 820 g | 164,000 | 100 | 100,000 |
0.01 g | 820 g | 82,000 | 100 | 100,000 |
0.02 g | 820 g | 41,000 | 100 | 100,000 |
0.05 g | 820 g | 16,400 | 100 | 100,000 |
0.1 g | 820 g | 8,200 | 5,000 | 100,000 |
0.2 g | 820 g | 4,100 | 5,000 | 100,000 |
Bold and italicized text denotes values that exceed Table 3 parameters for Class II scales. |
The lightest load expected to be weighed on the scale in the above example is 1 g. The weighing of light loads results in relatively large errors as referenced below in UR.3.1. Recommended Minimum Load, due to rounding of the scale division, d. The way e and d are identified in Table 8. Recommended Minimum Load must be considered in this context.
NIST HB 44 UR.3.1. Recommended Minimum Load. A recommended minimum load is specified in Table 8. Recommended Minimum Load since the use of a device to weigh light loads is likely to result in relatively large errors.
Table 8 Recommended Minimum Load
Class
Value of Scale Division
(d or e*)Recommended Minimum Load
(d or e*)II
0.001 g to 0.05 g
20
II
≥ 0.1 g
50
*For Class I and II devices equipped with auxiliary reading means (i.e., a rider, a vernier, or a least significant decimal differentiated by size, shape or color), the value of the verification scale division “e” is the value of the scale division immediately preceding the auxiliary means. For Class III and IIII devices the value of “e” is specified by the manufacturer as marked on the device; “e” must be less than or equal to “d.”
When determining the recommended minimum load for a scale where e = d, the interpretation of this table is straightforward:
The minimum value for e determined from the example above is 0.01 g. Per Table 8 the recommended minimum load is 20 d, which equates to 0.2 g. This value is smaller than the expected minimum load to be weighed (1 g) in the example. So, in relation to this requirement, an e of 0.01 g is acceptable. If the maximum value for e of 0.1 g is used, as determined above, per Table 8 the recommended minimum load is 50 d. This equates to 5 g which is larger than the expected minimum load to be weighed in the example. So, in relation to UR.3.1. and Table 8, an e of 0.1 g is not acceptable.
A more complicated scenario requires further examination of this table. Because of the placement of the asterisk on the e in both the middle and right columns of Table 8 and the language associated with it (bolded for emphasis), as currently adopted in NIST HB 44, the language in this table specifies using e as the value for the recommended minimum load when e ≠ d. When a scale is configured in this way, rounding still occurs based on d. But, because of the placement of the asterisk, the table effectively references e in both the middle and far right columns.
Therefore, when a scale is configured with e ≠ d, and e is between 0.001 g and 0.05 g, the recommended minimum load is 20 e. When e ≥ 0.1 g, the recommended minimum load is 50 e. Effectively making the recommended minimum loads the same values as when e = d. Based on the minimum value of 0.01 g, the recommended minimum load is 20 e, which equates to 0.02 g. Based on the maximum value for e of 0.1 g, the recommended minimum load is 50 e, which equates to 5 g. Again, it has been determined that 0.01 g is an acceptable value for e, while an e of 0.1 g is not acceptable. See the table below.
Verification Scale Division | Scale Division (d) | Table 8-Value of Scale Division | Table 8-Recommended Minimum Load | Recommended Minimum Load in g | Minimum and Maximum Load |
---|---|---|---|---|---|
Scales Configured with e = d | |||||
0.01 g | 0.01 g | 0.001 g to 0.05 g | 20 d | 0.2 g | Min: 1 g
Max: 170 g |
0.1 g | 0.1 g | ≥ 0.1 g | 50 d | 5 g | |
Scales Configured with e ≠ d | |||||
0.01 g | 0.00[1] g | 0.001 g to 0.05 g | 20 e | 0.2 g | |
0.1 g | 0.0[1] g | ≥ 0.1 g | 50 e | 5 g |
The markings in the above pictures indicate a “Min” of 0.5 g, when e = 0.1 g, and a “Min” of 0.02 g, when e is 0.01 g, respectively. This is based on requirements in OIML R 76 Non-automatic weighing instruments which specify that the minimum capacity, analogous to NIST HB 44’s recommended minimum load, be marked on the device. In OIML R 76 the Min is based on d when e ≠ d. As you can see, the scales in bold in the lower part of the table above have a different value than the marked “Min” because NIST HB 44 specifies using e instead of d, when e ≠ d. This may cause confusion for both the operator of the device and the weights & measures inspector. This is a subject that needs further consideration by the weights & measures community.
The price of a commodity is also relevant to both the selection of the appropriate scale division and the rounding of d. The following table shows the commodity, its unit price ($), the value of the scale division (d), the price per scale division ($ per d), and the dollar value of the rounding error that may occur during each weighment (Maximum rounding error). To simplify this discussion, the commodities from the example above and a scale configured with e = d will be used as the basis for the following table:
Commodity | $ | d (e) | $ per d | Maximum rounding error | Recommended Minimum Load |
---|---|---|---|---|---|
Persian Saffron | $4.20/g | 0.1 g | $0.42 | $0.21 | 5 g |
Persian Saffron | $4.20/g | 0.01 g | $0.04 | $0.02 | 0.2 g |
Tellicherry Peppercorns | $0.12/g | 0.1 g | $0.01 | $0.005 | 5 g |
Tellicherry Peppercorns | $0.12/g | 0.01 g | $0.001 | $0.0005 | 0.2 g |
What does this table reveal? Comparing the rounding error associated with the price of the commodity aids in determining the appropriate scale division. In the example, the typical amount of saffron purchased is expected to be around 1 g to 2 g. A purchase of 2 g would cost $ 8.38. The maximum rounding error associated with a d = 0.1 g is $0.21, which is 0.25 % of the purchase price. A purchase of 170 g of peppercorns would cost $ 20.40 with a maximum rounding error of $ 0.005 for a d = 0.1 g, which is 0.025 % of the purchase price. For the peppercorns, a strong case is made that a 0.1 g scale division is suitable. However, there are still concerns since the scale might be used for both saffron and peppercorns. The recommended minimum load remains an issue. If the scale used in this transaction has an e = 0.1 g, the recommended minimum load for this scale is 50 d or 5 g. The amount of saffron in this transaction, which is the largest amount expected to be sold, is less than half the recommended minimum load.
This table has various values for d (e).
Commodity | $ | d (e) | $ per d | Rounding error | Recommended Minimum Load |
---|---|---|---|---|---|
Persian Saffron | $4.20/g | 0.1 g | $0.42 | $0.21 | 5 g |
0.05 g | $0.21 | $0.11 | 1 g | ||
0.02 g | $0.08 | $0.04 | 0.4 g | ||
0.01 g | $0.04 | $0.02 | 0.2 g |
Based on the 1 g to 2 g increments the example specified, an e of 0.05 g, 0.02 g, or 0.01 g would meet the recommended minimum load requirement and have a reasonable rounding error.
Computing Capability. Although the example only mentioned two specific commodities, it does mention that several items will be sold from bulk. To facilitate efficient transactions and reduce the chance of calculating an incorrect total price, selecting a scale with computing capability or that can be interfaced with a “cash register” to create a Point-of-Sale (POS) System may be advantageous. Currently, a Class II Computing Scale does not appear to be available for commercial transactions. Thus, considering a scale that can be interfaced to create a POS system is the primary focus. While there are still some POS systems that consist of a cash register that can be connected to a scale to process a transaction, the most common POS system consists of several not-built-for-purpose devices such as a monitor, a computer with POS software typically connected to a server, a printer, and a keyboard, the combination of which is referred to as an “electronic cash register” which is connected to a scale. Most commonly, POS software is developed to interface with Class III scales. If the software may be interfaced with a Class II scale, then certain aspects must be verified which may be less relevant than when considering a Class III system.
Direct or Indirect Sales. Will the scale be used in a direct-sale application (where the customer is present) or an indirect-sales application, such as pre-packaging?
If used in direct sales, the customer and operator must be able to view the weighing transaction from a reasonable position, per G-UR.3. in the General Code of NIST HB 44. That may mean the scale is properly positioned or has more than one weight display, possibly a secondary display that is not the primary indication.
If used in a pre-packaging application, tare must be accounted for in some fashion. It can be preprogrammed and associated with a unit price, deducted using a tare key, or deducted by some other method, such as a zero key.
Environment and Other Factors. The environment in which a Class II scale is used must be stable. The slightest air movement or vibration can affect the scale's accuracy. It should not be located near any HVAC vents, fans, areas with heavy foot traffic, or equipment with moving parts. The support structure for the scale should be sturdy and, at a minimum, able to support the weight of the scale plus test weights to capacity.
Relationship of e and d. There are many requirements that apply to Class II scales. For the purposes of this article, only the requirements applicable when e ≠ d will be considered. Per the specifications in S.1.2.2.1. Class I and II Scales and Dynamic Monorail Scales, only certain scales, including Class II scales, are allowed to operate with e ≠ d, but there are limitations. When a scale is configured in this manner, d must be less than e but be no less than 1/10 of e. The formula in NIST HB 44 specifies:
$$d < e \leq 10 d$$
In addition, e must be some value of 1, as specified by the equation e = 10^{k}.
The following tables illustrate these principles:
When k equals | expressed as | e is equal to |
---|---|---|
-3 | 10^{-3} | 0.001 |
-2 | 10^{-2} | 0.01 |
-1 | 10^{-1} | 0.1 |
0 | 10^{0} | 1 |
1 | 10^{1} | 10 |
2 | 10^{2} | 100 |
3 | 10^{3} | 1 000 |
When e is: | d can be: | ||
---|---|---|---|
0.001 | 0.0001 | 0.0002 | 0.0005 |
0.01 | 0.001 | 0.002 | 0.005 |
0.1 | 0.01 | 0.02 | 0.05 |
1 | 0.1 | 0.2 | 0.5 |
10 | 1 | 2 | 5 |
100 | 10 | 20 | 50 |
1 000 | 100 | 200 | 500 |
When e and d are both displayed simultaneously, d must be differentiated in some manner. One way to accomplish this (e.g., adding brackets around d) is illustrated below:
Tolerance Application. No matter what class of scale is being tested, tolerance is always determined by e. Item SCL-23.4, on the 2024 NCWM S&T agenda proposes amendments to clarify this principle further. Tolerance application is more complicated when a scale is configured with e ≠ d as shown in the table below. An abbreviated version of Table 6 is included as a reference:
Verification Scale Division | Scale Division | Capacity | n |
---|---|---|---|
0.1 g | 0.01 g | 820 g | 8,200 |
Tolerance in (Verification) Scale Divisions | |||
---|---|---|---|
1 | 2 | 3 | |
II | 0 – 5000 | 5001 – 20000 | 20001+ |
To test this scale at 5000 e, a test load of 500 g (5000 e x 0.1 g) is applied. If the scale displays 500.12 g the error is + 0.12 g. To convert to e, this error is divided by 0.1 g, which is equal to 1.2 e. The tolerance is +/- 1 e at this test load so the scale exceeds tolerance by 0.2 e. To test the scale at 20000 e, a test load of 2000 g is applied. If the scale displays 1999.74 g the error is - 0.26 g. Converted to e, the error is -2.6 e. The error exceeds tolerance by 0.6 e.
Appropriate test standard classification. In reference to testing, to ensure the device under test is given the benefit of the tolerance allowed, it must be tested by the appropriate test standard. For Class II scales, the class of test weight is different from the more common Class III and III L scales, which can be tested appropriately with NIST Class F test weights (or equivalent ASTM or OIML class weights). Because of the increase in the use of Class II scales in commercial applications and the fact that NIST Class F weights are not suitable test standards for Class II scales, NIST OWM updated NIST Handbook 105-1 in 2019 to add references to ASTM E617 and OIML R 111-1. These standards include weight classifications that specify tolerances that meet the criteria in NIST HB 44, Appendix A, 3. Testing Apparatus. The table below includes test standard classifications that are appropriate for Class II scales and is adapted from NIST HB 105-1 (2019):
Classification of Weighing Device Tested | ASTM Accuracy | OIML Accuracy |
---|---|---|
Class II | 1, 2 |
For a more in-depth discussion of the revisions to NIST Handbook 105-1 (2019), please see the following technical articles:
Please also see the Weighing and Scales FAQs for a more in-depth discussion of the difference between the scale division, d, and the verification scale division, e.
A recorded webinar, “Precision Scales Overview,” will soon be available on the OWM e-Learning Resources webpage. It will include a more detailed discussion of the topics covered in this article.
Please contact Loren Minnich at loren.minnich [at] nist.gov (loren[dot]minnich[at]nist[dot]gov) or Jan Konijnenburg at jan.konijnenburg [at] nist.gov (jan[dot]konijnenburg[at]nist[dot]gov) for any further questions.