Before considering using a balance or perform a weighing scale verification, one primary requirement is to know the tolerance limit. The user should determine the tolerance limit in consideration of their process, but this is not always the case.

As per my experience, most users rely on the manufacturer’s specifications as the basis of their tolerance limit. But one problem I see is that it does not show the tolerance limit or accuracy rating in their specifications (user manual).

How can you verify the balance if the tolerance is not known or given in its specification?

Determining the tolerance of the balance is a bit tricky if you do not know certain terms and parameters dedicated to a weighing scale.

In this post, I will share with you how to check the accuracy of the weighing scale when its accuracy or tolerance limit is not given. I will share the calculations here based on the OIML R 76-1 2006 Guide.

I will discuss the following topics:

- Types of Balances and Its Accuracy Class
- What is the Verification Scale Interval ‘e’?
- How to Calculate the Value of the Verification Scale Interval ‘e”?
- How to Choose the Appropriate Standard Weights Used for Balance Calibration or Verification?
- How to Perform Verification of Weighing Instruments Before Starting Calibration

I hope this post will help you learn how to use digital weighing scale specifications to calculate tolerance limits and other important parameters in order to perform properly a balance verification and calibration.

**Types of Balances and Its Accuracy Class **

Before we perform balance calibration and verification, it is important to familiarize ourselves with the different types of non-automatic weighing scales.

There are so many kinds of scales, and honestly , It is sometimes confusing if you are not familiar with it.

If you are familiar with the balances, you can easily determine the accuracy class and therefore its MPE (Maximum Permissible Error) which is our goal in this post.

Different types of balances have their own specific number of resolution and accuracy classes. It is important to know the accuracy class because it will help you determine the tolerance limits of the balance.

To easily understand, see the below table which is based on table 1 of NABL doc 129.

Observe that the higher the Accuracy Class, the more decimal places before the significant digit. For example, during the calibration of analytical balance, you easily know that it has 4 decimal places, and it falls under Class I accuracy class.

It is easier to determine the types of balance when you know its accuracy class and number of decimal places and the other way around.

Every type of balance has its own accuracy class and therefore, a tolerance limit or an mpe (maximum permissible error). This is comparable to a pressure gauge where its accuracy class or grade gives you a direct accuracy rating.

But in a balance or weighing machine, it is different, the accuracy class is only a part of the requirement in order to calculate the mpe or tolerance limit. Therefore, it is important to familiarize ourselves first with the accuracy class of a balance.

Below are the symbol used for each accuracy class marked on different weighing scales as per OIML R76-1:

Now that we have determined the different types of Non-Automatic Weighing Scales (NAWS) with its accuracy class, we are now ready to for the next requirement, to determine the “Verification Scale Interval – e”

**What is the Verification Scale Interval ‘e’?**

If you noticed the specifications of most balances in their user manual, you will see a letter ‘e’ alongside with letter ‘d’.

My first time exposed to the ‘e’ and ‘d’ term makes me confused on their use, what I do is just ignore the ‘e’ term. But now that I understand their difference, I see that the ‘e’ term has more use than the ‘d’ term.

Let us see the definition of verification scale interval ‘e’ and the actual scale interval ‘d’ to understand better.

**Actual scale interval **– the symbol is **‘d’** which is commonly known as the resolution, readability or the smallest change that we can observe. As per OIML definition, it is the difference of two consecutive indicated values.

**Verification Scale Interval**– uses the symbol **‘e’**– which is defined under OIML as “Value, expressed in units of mass, used for the classification and verification of an instrument.”

Verification Scale Interval ‘e’ is a scale interval used for verification purposes, hence the term “verification’ with it.

This means that during verification, in order for us to determine the classification and tolerance of our balance, we need the value of ‘e’, the verification scale interval, which is based on the actual scale interval, the ‘d’, or the resolution.

You can understand more the use of the ‘e’ by referring to below table.

The table we just seen above shows the requirements for every accuracy class. If you know the ‘e’, you can determine:

- The minimum capacity of the balance, some balance specifications, minimum range is not given, therefore, we need to calculate in order to determine the minimum range where the balance can perform its best.
- The accuracy class of the balance
- The mpe or the tolerance limit of the balance

Once you have determined the ‘e’ value, you can now calculate its tolerance limit then perform a verification.

Usually, e = d on class III and IIII balances (ordinary balances)

**How to Calculate the Verification Scale Interval ‘e”?**

Below are ways to calculate the value of **‘e’**.

Determine the resolution ‘d’, then;

For example:

balance resolution ‘d’ =0.001 g

e =10(d) = 10 (0.001)**e=0.01 g**

Now that you have calculated the value of ‘e’. You can now calculate and determine the tolerance limit or the *mpe* of the balance. But before we will determine the *mpe*, let us first learn how to choose the suitable standard weights to be used for our verification or calibration.

**How to Choose the Appropriate Standard Weights Used for Balance Calibration or Verification?**

Before we perform the calibration or verification, it is important to determine first the suitability of standard weights that we will use for the balance.

Here is a simple formula to use as per OIML guide.

“*They shall not have an error greater than 1/3 of the maximum permissible error of the instrument for the applied load*“.

The error that is referred to here is the measurement uncertainty value. The expanded uncertainty found in the calibration certificate of the standard mass. This means that the measurement uncertainty of the standard weights to be used should be within the limits if the *mpe* of the balance will be divided by 3. See below the relationship/equation.

.**Example:**

Balance mpe: 0.01 grams

0.01/3 = 0.0033 grams.**>> **This means that the measurement uncertainty of the standard weights should not exceed 0.0033 grams.

To make it more simple, here is a summarized guide from UKAS Lab 14.

For example: A 500 g capacity balance with a resolution of 1 g, a class M3 standard weights is appropriate or has enough accuracy to be used for calibration or verification.

**How to Determine the Tolerance Limit or MPE of the Balance?**

Now that we know the value of ‘e’, and the accuracy class of the balance, we can easily calculate the mpe that we need.

By using the tables below, we can now determine the tolerance of our balance.

But another value, the ‘m’ value is now needed. ‘m’ is the value of ‘Mass’ but expressed in “Verification Scale Interval**s** ‘n’. To calculate ‘m’, below is the formula:

After we have determined m, we can now choose the multiplier for our ‘e’ (first column) and then calculate our mpe or tolerance limit, see below table.

**Example 1:**

Given the specifications above, you will notice that accuracy or tolerance limit is not given. Below are the specs we need.

**Max = 520 gd= 0.001 g**

Verification Scale Interval ‘e’ and Accuracy Class is not given, but based on its resolution, this is a Class II balance which is a precision balance with high accuracy based on the table above (Types of Balances).

First, let us calculate ‘e’

Formula:

e = 10d; where d = 0.001 g

= 10 (0.001)**e = 0.01 g**

Now that we have the value of e, we need to refer to the table above:

We need now the accuracy class and the Verification scale intervals ‘n’

n = Max/e = m

= 520/0.01**n = 52000**

Now, based on the table below, we can see where the value of m =n= 52000 will fall, which is under class II with mpe = 1.5e

mpe=1.5(0.01)** mpe= +/- 0.015 grams = tolerance limit**

We can also calculate the minimum range, based on the given formula above where,

Min =20e

=20 (0.01)**Minimum range = 0.2 grams**

Now that we have calculated the tolerance, it is now time to perform the balance verification.

**Example 2**, where value of ‘e’ is provided

Refer to the photo below:

The above specifications are easier to calculate because the accuracy class and ‘e’ are already given. We have,

Given:

Accuracy Class = III

Max = 60 kg

Min= 0.4 kg

d=0.02 kg

e=0.02 kg; where e=d in a class III balance

Calculate:

1. The value of n, where n= max/e

= 60/0.02

** n = 3000**

- The mpe, where mpe=1.5e (see below table)

=1.5(0.02)

**mpe = 0.03 kg**

**How to Perform Verification of Weighing Instruments Before Starting Calibration**?

Before calibration of balance is performed, the initial task is to perform first the verification of balance then afterwards an adjustment if needed. This makes it different to other instruments where calibration is first performed before verification.

One reason is that there is no point in performing a balance calibration if you know in your results that the readings are far from the nominal of the standard weights used.

This is why initial verification is performed then an adjustment follows.

Once we determined standard weights to be used, the next is to perform a balance verification. If we say verification, we will perform a simple test using a known mass, then we will compare the display of the balance with the nominal value of the standard weights. For the results to be acceptable, they should be within the *mpe* or tolerance limit of the balance.

The initial verification is performed by determining 80% capacity of the balance. After warm up time and exercising or preloading the pan, we then use a standard weight that is equal or near the 80 % capacity of the balance.

For example:

Balance Max Capacity =3750 g

Tolerance Limit=0.1 g

Standard weights to use is 80% of 3750 = 0.8*3750 = 3000g, therefore, you can use the exact nominal value which is 3000 g standard weights.

As found value = 2999.86

Error = 2999.86-3000 = -0.14

Based on the results and tolerance limit , it is a** FAIL**, therefore we need to perform adjustment

We call this verification “Adjustment of Error Close to Max”. We can perform the adjustment either internal adjustment or external adjustment. (See the difference of internal and external adjustment in this link>> Balance adjustment)

But before performing the verification process, it is assumed that you already know the MPE or the tolerance limit of the balance.

To calculate the accuracy of a digital weighing scale, you can check my other posts here>> Accuracy

**Conclusion**

In order to perform verification of balance, it is important to determine the value of ‘e’, which is known as the ‘verification scale interval’

Verification scale interval ‘e’ is comparable to the resolution ‘d’, which is the smallest display you can read. But ‘e’ is used for determining the mpe or tolerance limit and the classification of the balance (accuracy class) for verification purposes. Calculations to determine e and the tolerance limit are discussed.

In this post, I have presented the following:

- Types of Balances and Its Accuracy Class
- What is the Verification Scale Interval ‘e’?
- How to Calculate the Value of the Verification Scale Interval ‘e”?
- How to Choose the Appropriate Standard Weights Used for Balance Calibration or Verification?
- How to Perform Verification of Weighing Instruments Before Starting Calibration?

Please understand that this is just a recommendation if ever you do not have a basis for your tolerance limit. You should verify its suitability before implementation. The calculation of the tolerance limit should be based on your own process and as per the actual performance of the balance.

**If you like this article, I appreciate if you could share, leave a comment and subscribe.**

You can also connect with me on my Facebook page.

Best Regards,

Edwin

## 46 Responses

## Sriyani Chandrika

Thanks your post. It is very useful to me. I am working in NML Sri Lanka.

Can you post intermediate checking method for electricity meters / Energy meters

## edsponce

Hi Sriyani,

You are welcome. Thanks for visiting my site.

I will include in my list your concern in my future posts.

Happy to connect with a fellow Metrologist.

Best regards,

Edwin

## Joshua Keter

Elaborate!

I head a calibration Lab in Kenya and this soo useful to me

## edsponce

Hi Joshua,

I am glad that this post is useful to you.

Thanks for commenting and reading my post.

Best regards,

Edwin

## Ben

Hello,

What do you meant by Class III “Or Above”? does Above mean better or does it mean Class IV ?

Thanks,

## edsponce

Hi Ben,

‘Above’ means class IV, next to class III, where accuracy is lesser, therefore, the tolerance limit is getting higher.

Thanks for reading my post.

Edwin

## Vinod Kumar

Dear Mr. Edwn, Thanks for your valuable post, We have an analytical balance at worplace with following specs Mettler Toledo/TE204, Max. capacity 220g, Minimum Capacity: 0.1g, e:1mg, d:0.1mg. I am doubtful about e and d value, this balance resolution is 1 mg (displayed 1.000 g @ 1 g standard weight). if we call d as resolution then this balance not meets the standard norms. Your comment is required in the clarification of the same.

## edsponce

Hi Vinod,

The specification is ok. Have you checked the user manual, maybe there is a setting to adjust the full resolution to 0.0001g. This can be done to most high-end balances.

But, if that is really the exact specifications for ‘d’, then you need to calculate the ‘e’ based on the actual resolution that you have.

I hope this helps,

Edwin

## Salim Muktar mohammed

Very educative. Intertwining Relationships in mass calibration explained in details. e, d, m, MPE, class of the balance and weight, uncertainty values, and initial verification. What more do you need?? Thank you Edwin

## edsponce

Hi Salim,

You are welcome.

Thank you for the encouraging comments. I appreciate the time reading my post.

Best Regards,

Edwin

## Robbie

Very informative with fundamentals of measurement.

## edsponce

HI Robbie,

Thank you. I am glad you liked it.

Edwin

## Robbie

Hi Edwin,

When n=52000, per table, it also falls under Class-I where 50000 <m<=200000. Please clarify why a Class-II is being considered? Even per your first table of balances and accuracy class, it should fall under Class-I.

## edsponce

Hi Robbie,

The 520g balance with d=0.001 will fall under Class II based on its resolution. See again the very first table where 0.001 is under Class II with 2 to3 decimal places.

Since we already know it is under Class II, we will match it with its n=52000 aligned with 1.5e.

I hope this helps, thanks for reading my post.

Thanks and regards,

Edwin

## Robbie

On the same note, what class and MPE should be for a 120g max capacity balance with d = 0.1mg?

## edsponce

Hi Robbie,

See below:

a 120g max capacity balance with d = 0.1mg

– d=0.1 mg = 0.0001g resolution fall under

Class Ibalance.– e=1mg;

– n=120/0.001 = 120,000

–

MPE=1.0e = 1.0 (0.001) = 0.001gBest regards,

Edwin

## Oksana Klueva

I have a dual range Class I balance with full range of 120 g (d=0.1 mg) and fine range of 41 g (d=0.01 mg). Do I need to calculate MPE separately for both ranges? if I use fine range max capacity of 41 g, then e = 1 mg regardless but m =41 000 mg/1 mg = 41,000. That gives an MPE = 0.5 e = 0.5 mg. Should I use the large MPE or use both in the corresponding range?

## edsponce

High Oksana,

Since your balance is a dual-range, then yes, you need to calculate the MPE separately.

I am glad that you have followed my instructions. MPE for 120g is 1mg while MPE for 41g is 0.5mg.

Thanks for visiting my site.

Edwin

## Vinod Kumar

Dear Edwin,

Extraordinary efforts being put by you to create this blog. Very aligned topic of uncertainty in measurement for weighing scales will be helpful for many of people who are in the field of calibration. Expected short and quick post on the same from your side. Again thanks a lot for sharing useful information.

## edsponce

Hi Vinod,

You are welcome and thank you as well for the heartwarming comments. I will consider in my future posts your recommendations.

I appreciate the time reading my posts.

Have a safe day,

Edwin

## Mohammed Fahad

Hi Edwin,

Extremely useful and informative post. you very concisely and precisely elaborated the topic. it was easy to read and understand although I have a suggestion – the statement “Class III and above” is a bit confusing. A footnote clarifying the statement would be quite valuable. your effort is highly appreciated. Hope to meet you someday.

## edsponce

Hi Mohammed,

Thank you for your inputs, I appreciate it. I will check and consider it.

Meeting you would be a pleasure.

Best regards,

Edwin

## Ahmad Feiz

Greetings

In the following example where you have confirmed the scales, if you multiply 80% by 6000, it becomes 4800 grams, you get 3000 grams?

Balance Max Capacity = 5400 g

Tolerance Limit=0.1 g

Standard weights to use is 80% of 5400 = 0.8*6000 = 3000g, therefore, you can use the exact nominal value which is 3000 g standard weights.

As found value = 2999.86

Error = 2999.86-3000 = -0.14

## edsponce

Hi Ahmad,

Thanks for letting me know, already corrected.

Appreciate the time reading my post.

Have a nice day,

Edwin

## EDUARDO

EXCELENTE PUBLICACIÓN, PERO ESTÁ MAL SI APLICO d=e para todas las clases de balanzas???

## edsponce

Hi Eduardo,

To determine the Tolerance Limit of the balance, we need the value of ‘e’. For lower class balances like Class III and above, d=e.

But if in your process where you are using class I and II, and you accept a tolerance limit with e=d, then it is OK. But make sure that the resulting Tolerance limit is accepted and documented as your tolerance limit.

I just translated your message, I hope this helps,

Edwin

## Divya

Dear Edwin

is tere any importance of linearity in verification of balance

## edsponce

Hi Divya,

Yes, this is one of the characteristics or performance of a balance that you should know if you are using the balance in different ranges. You will face an issue at higher ranges if the balance has a problem with linearity.

Linearity means that it has the same error or no error at all at increasing loads. If error is increasing with increasing load, then there is a problem with linearity that you need to fix. This error should be within acceptable range or specifications if you include it as part of your verification.

I hope this helps,

Edwin

## Krish

Sir,

Excellent information…Thank u very much…

## edsponce

Hi Krish,

You’re welcome,I am glad you liked it.

Thanks for reading.

Edwin

## Alfred V. Lomat

Thank you a lot Sir!

## edsponce

You’re welcome, Thanks for reading my posts.

Best regards,

Edwin

## MOHAMED

Thanks from Libya,I am performing calibration and your information helped alot.

Could you please send me email so we can keep on touch .

m_ammar_t@yahoo.co.uk

## edsponce

Hi Mohamed,

You are welcome. I am glad this article has helped you.

This is my email add: edwin@calibrationawareness.com

Thanks for visiting my site. Any concerns you have just message me.

Regards,

Edwin

## Jay

I run a processing plant that utilizes weighing scales. This has been very useful in helping me prepare procedures for receiving inspection of scales. Just curious, this article appears to be focused on digital scales, but from what I understand, the information in this specific article can also be applied to analog scales.

## edsponce

Hi Jay,

Yes you are correct, this is focused on digital scales where ‘e’ term is given which confuses most of the users. But also applicable to some analog scales that follows the accuracy classes.

You may also check other references like ‘NIST Handbook 44’ for other tolerance limits.

I am glad that this article has been useful to you. Thanks for reading my posts.

Best regards,

Edwin

## divya

Dear Edwin,

Do we need to perform daily checks for weighing balance.Is it mandatory as per ISO17025.If so, which all range of a balance we need to check and the acceptance criteria

divya

## edsponce

Hi Divya,

Yes, it is mandatory to check the weighing balance as per 17025 or ISO 9001. It will fall under intermediate check. But the frequency of checking depends on the criticality of use or as per your procedure. The range and acceptance criteria are also based on your usage, no need to test all ranges as long as you check the range you use. Acceptance criteria may be based on manufacturer specs or you can use the procedure that I have presented here.

I hope this helps.

## divya

Dear Edwin

Do we need to do calibration checks of weighing balance idaily.If so what will be the acceptance limit we have to take’s it th error in the calibration certificate .

thanks

divya

## edsponce

Hi Divya,

The checking depends on the procedure you set, there is no fixed requirement. The acceptance limit is usually based on the manufacturer specifications or the procedure that I presented here if you accept to follow it. You can also provide your own acceptance limit based on your process.

I hope I answered your concern.

Thanks for reading my post.

Edwin

## Suradetch

Dear, Mr. Edwin

Thank you very much your post helps me a lot.

From calculated tolerance limit = +/-0.015 g

and the error from calibration certificate = 0.01 g but uncertainty value is 0.028 g (28 mg)

So how should to determine the MPE value to be consistent with this uncertainty value.

Thank you

## edsponce

Hi Suradetch,

You are welcome.

Your MPE has nothing to do with the uncertainty results in this case. That is already the result provided by the calibration lab unless you perform the determination of your tolerance limit where you included the uncertainty value in the first place during the calculation of your tolerance limit.

Based on your result, it will become a problem when the large uncertainty value is included in the measurement results during verification, which will result to a ‘Fail’.

The large uncertainty value provided by the calibration lab means that:

1. Repeatability of your instrument is not good.

2. The standard used for calibration does not meet the 4:1 accuracy ratio, meaning, accuracy of the standard is bigger than the UUT.

3. The uncertainty value of the standard used is large.

4. There is a mistake during uncertainty estimation or calculation.

The best thing you can do are:

The best thing you can do are:

1. Adjust your tolerance limit.

2. Recalculate tolerance limit by including the measurement uncertainty in the calculation.

3. Call your calibration lab and verify if they can recalculate their measurement uncertainty with regards to your tolerance limit.

4. Look for a calibration lab that has a smaller uncertainty value – This will cost more but this is the best solution as per my analysis on your results.

I hope this helps.

Edwin

## Nazanin

I can’t say thank you enough, you can’t imagine how you helped me to understand what I’ve read on OIML but I couldn’t completely figure that out,

THANK YOU AGAIN

## edsponce

Hi Nazanin,

You are welcome, I am glad that this article has helped you.

Thanks for the comment.

Best regards,

Edwin

## Phil

Great article and very helpful, I would just like the know the source for the formula n=m=MAX/e, it is not mentioned in OIML R 76-1 2006 Guide as far as I can tell.

Thank you 🙂

## edsponce

Hi Phil,

Thanks for visiting my site.

The equation for ‘m’ is not directly shown in the standard but it is stated in the table that ‘m’ is expressed in the number of verification scale intervals which is the ‘n’.

I hope this helps,

Edwin