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Accuracy, Error, Tolerance and Uncertainity

December 29, 2020


   Calibration involves so many terms that we always use or read during the measurement process. Knowledge in these terms is the key to proper understanding and execution of measurement results which is an important part of calibration awareness training.


In this blog, we will be discussing accuracy, error, tolerance, and uncertainty and their relationships.



As per JCGM 200 and 106: 2012, below are the actual definitions:

1.    Accuracy = closeness of agreement between a measured quantity value and a true quantity value of a measurand

2.    Error or measurement error = measured quantity value minus a reference quantity value

3.    Tolerance =difference between upper and lower tolerance limits

4.    Uncertainty or measurement uncertainty = non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used- make more meaningful


It is the closeness of UUC results to the STD (true) value. This ‘closeness’ is usually represented in percentage value (%) and can be shown in the same unit by converting it into an error value ( %error). The more close the percentage value to ZERO (0%), the more accurate. Accuracy is more on a qualitative description which means that it does not present an exact value. It is equivalent to a percent error (%error). This is where the value of error will be used.


It is simply the difference between the UUC and STD results after calibration. It has the same unit as the measured parameter.


It is the maximum error or deviation that is allowed or accepted in the design of the user for its manufactured product or components. Tolerance is a range of values that is acceptable or permitted by the user from the result of the process or product measurement. It is the permitted error that is:

1.    Calculated from the process design by the user

2.    Prescribed by regulatory bodies (based on Accuracy Class)

3.    Manufacturer specifications (based on Accuracy)

The formula is Upper limit – lower limit (UTL-LTL). UTL or LTL is the value based on tolerance limits. Tolerance limits = Tolerance/2. Tolerance Limits are provided either by manufacturer or process requirements. If we perform a measurement, the value of the tolerance limit will tell us if the measurement we have is acceptable or not. If you know the calibration tolerance limits, it will help you answer the questions like:

1.How do you know that your measurement result is within the acceptable range?

2. Is the final product specification pass or fail? 3. Do we need to perform adjustments?

“The wider the tolerance Interval, the more product or measurement results will pass or accepted.”


Uncertainty or Measurement Uncertainty is defined as the quantification of the doubt. There is always a doubt that exists, an error included in the final result that we do not know, therefore, there are no perfectly exact measurement results, Why do we have uncertainty or doubt in our measurement? Some of the main reasons why we have doubt or uncertainty in measurements are:

1.    Inadequate knowledge of the effects of the environmental conditions on the measurement

2.    Personal bias in reading analog instruments, an example is the resolution or smallest value that you can read

3.    Inexact values of measurement standards and reference materials

4.    Approximations and assumptions incorporated in the measurement method and procedure

5.    Variations in repeated observations of the measurand under apparently identical conditions – Repeatability

“The smaller the measurement uncertainty, the more accurate or exact our measurement results.”

Accuracy Versus Error

Accuracy is for gauging how small/large the error is (a qualitative description),  while the Error is the actual representation of accuracy in the same units as the measured parameter (measurand). In other words, the error shows the quantity of accuracy in the unit of measurement used. Accuracy and error have opposite relationships (indirectly proportional) but they are directly related to each other. An accuracy is a qualitative form, meaning no exact value or measurement result is presented, only a presentation (usually in percentage form) of how good or bad or how far and near but no exact value, while error shows the absolute value or actual value. In order to show the exact or absolute value, we need to use the error. The error shows the exact distance of the measurement result from the true value.

Accuracy Class and MPE

A Manufacturer Tolerance Value At this point, accuracy can be used as a Tolerance based on manufacturer specifications. We call this type of accuracy the Accuracy Class or Grade. Then from the accuracy class, it is calculated to its equivalent error which is called the MPE (maximum permissible error) as required by standards like ASTM and  ISO or manufacturer’s specifications. This is then used as the tolerance limits, and afterward, the tolerance value.

Error vs Uncertainty

As we know now, Error is the difference between UUC – STD reading. The smaller the error, the more accurate the measurement results. UUC -STD = error Any error that we know can be corrected. From calibration certificate results, where a standard value is given, we can now determine the error. And since the error is determined, we can correct it by either adding or subtracting the correction factor which is the opposite of the error. Correction = STD-UUC. Uncertainty is the ‘range of values’ where the true value or actual location of the measurement results (UUC) lie, while the Error is the ‘exact result’ of the difference between the UUC and STD which shows how accurate the measurement result is by showing the actual distance to the true (STD) value. Uncertainty is a boundary within the measurement results to show the range of its actual location based on a given confidence level (95%, k=2)). See the below photo.

The Difference  Between Tolerance, Error, and Uncertainty

1.    The Tolerance is the permissible value of errors that are limited by the upper and lower tolerance limits

2.    The Uncertainty shows the boundary or limits of an estimated error where the exact measurement result’s location.

Tolerance and Uncertainty As a Basis for Decision Rule as per ISO 17025:2017 Uncertainty is used or included when determining compliance with specifications as per the requirement of ISO 17025:2017. One way to tell if a product has passed or failed based on a given tolerance, a decision rule.

What is a Decision Rule?

As per ISO 17025:2017, clause 3.7, it is a rule that describes how measurement uncertainty is accounted for when stating conformity with a specified requirement. One way to account for measurement uncertainty is to include it in the measurement results. We will use it as if it is a tolerance limit within the measured value. Below are the decision rules

1.    If the results of our measurements are within the tolerance indicated including the uncertainty results, then it is a ‘pass’.

2.    If the results of our measurements are outside the tolerance including the uncertainty results, then it is considered  ‘fail’ or ‘out of tolerance’.

3.    If one of the uncertainty limits is outside the tolerance while the other limits are inside the tolerance limit, then it is not a pass or a fail, we call it ‘Indeterminate’. The decision now is based on the user.

The use of tolerance and uncertainty results to come up with a decision rule. The UUC results including the uncertainty are within tolerance and therefore, it is ‘Passed’ The Relationships Between Accuracy, Error, Tolerance, and Uncertainty – The Interpretation from a Calibration Result Accuracy shows the degree of closeness of a measurement result to the true or reference value. The degree of closeness from the reference value is presented in the actual value (not a percentage (%) of) through the calculated Error (UUC-STD). The error shows how the measurement results have deviated from the true value. While accuracy is calculated based on error and true value, Uncertainty is calculated based on the combined errors or inaccuracy of reference standards (STD) and the measurand (UUC). Uncertainty shows the range where the measurement results (UUC) actually located. An estimated location of true UUC value which is limited by the confidence interval (usually @ 95%, k=2). In order for the result to be acceptable, uncertainty results should stay within the tolerance limit.

Tolerance shows the permissible error of measurement results and it is the difference between the UTL and LTL (UTL-LTL).

These are the most used terms when it comes to reporting calibration results, understanding and creating a calibration procedure, or just simply understanding a calibration process. Their understanding is of utmost importance for understanding the process we are doing. We at General Tech Services provide calibration services in UAE and Saudi Arabia. Our aim is to ensure calibration with high accuracy, low errors, and uncertainty enabling an equipment’s highest performance and thus an efficient industry. We have the widest scope for Calibration in the Middle East.

Contact : Mathews@generaltechuae.com


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