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Absolute error is a term often used in various scientific and mathematical disciplines to quantify the difference between an estimated or measured value and its corresponding true or accepted value. It provides an objective measure of the accuracy or inaccuracy of a measurement or calculation. Understanding how to calculate absolute error is essential for researchers, engineers, and scientists to ensure the reliability and validity of their results. Whether it is in experimental measurements, statistical analysis, or mathematical modeling, the ability to determine absolute error is vital in assessing the precision and correctness of data. This guide will delve into the concept of absolute error, explain its significance, and provide step-by-step instructions on how to compute it accurately. By grasping the fundamentals of absolute error calculation, readers will gain a valuable skillset that can be applied across various domains and contribute to meticulous scientific inquiry.
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Absolute error is the difference between the measured value and the true value. [1] X Research Source This is a way to check the accuracy of the values when measuring. If you know the true and measured values, you can calculate the absolute error by performing a simple subtraction. However, if sometimes the true value is not available, you can take the maximum possible error as the absolute error. [2] X Research Source If you know the true value and the relative error, you can also work backwards to find the absolute error.
Steps
Use measured value and actual value


- Example: You are measuring the length of a football field. In Vietnam, the true value or accepted length of a professional football field is about 110 meters. Substituting the actual value of 110 into the formula, we have: Δx=x0−110{displaystyle Delta x=x_{0}-110} .

- Continuing the example above, if you measure the length of the football field as 107 m, this will be the measurement value. Substituting into the formula, we have: Δx=107−110{displaystyle Delta x=107-110} .

- In the football field example, we have: Δx=107−110=−3{displaystyle Delta x=107-110=-3} . So, the absolute error of the football field measurement is 3 m.
Use true value and relative error


- For example, if the relative error is 0.025, the formula becomes:0,025=x0−xx{displaystyle 0.025={frac {x_{0}-x}{x}}} .

- For example, if the given true value is 360 m, the formula becomes: 0,025=x0−360360{displaystyle 0.025={frac {x_{0}-360}{360}}} .

- For example:
0,025=x0−360360{displaystyle 0.025={frac {x_{0}-360}{360}}}
0,025×360=x0−360360×360{displaystyle 0.025times 360={frac {x_{0}-360}{360}}times 360}
9=x0−360{displaystyle 9=x_{0}-360}

- For example:
9=x0−360{displaystyle 9=x_{0}-360}
9+360=x0−360+360{displaystyle 9+360=x_{0}-360+360}
369=x0{displaystyle 369=x_{0}}

- For example, if the measured value is 369 m and the actual value is 360 m, we have: 369−360=9{displaystyle 369-360=9} . So, the absolute error is 9 m.
Use the maximum possible error

- For example, if the measured length of a road is 357 m, you will know the road is measured to the nearest meter. So, the measurement value is 1 m.

- Continuing the example above, if the unit of measurement is meters, the maximum possible error is 0.5 m. Therefore, the measure of the path length will be 357±0,5m{displaystyle 357pm 0.5m} . This means that the actual value of the path length may be 0.5 m shorter or longer than the measured value. Where this length is shorter/longer, the measurement value can be 356 or 358 m.

- In the example, if you find the measure of the road length is 357±0,5m{displaystyle 357pm 0.5m} then the absolute error will be 0.5 m.
Advice
- If the actual value is not given, you can take the accepted value or the theoretical value.
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
This article has been viewed 10,557 times.
Absolute error is the difference between the measured value and the true value. [1] X Research Source This is a way to check the accuracy of the values when measuring. If the true and measured values are known, you can calculate the absolute error by performing a simple subtraction. However, if the true value is not available sometimes, you can take the maximum possible error as the absolute error. [2] X Research Source If you know the true value and the relative error, you can also work backwards to find the absolute error.
In conclusion, calculating absolute error is a straightforward process that allows us to quantify the difference between an estimated or measured value and the true or accepted value. By subtracting the two values and taking the absolute value, we obtain a numerical representation of the deviation or discrepancy. Absolute error is an important tool in fields such as science, engineering, and statistics as it helps us evaluate the accuracy and precision of measurements and predictions. Understanding how to calculate absolute error provides a foundation for effectively analyzing and interpreting data, ensuring the reliability and credibility of our findings. Furthermore, absolute error allows us to communicate the level of uncertainty associated with our measurements and predictions, aiding decision-making and quality control processes. Overall, mastering the calculation of absolute error empowers individuals to improve their understanding of the validity and reliability of data, enabling them to make more informed and evidence-based conclusions.
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