PDF download Download Article PDF download Download Article

Absolute error is the difference between the measured value and the actual value. [1] It is one way to consider error when measuring the accuracy of values. If you know the actual and measured values, calculating the absolute error is a simple matter of subtraction. Sometimes, however, you may be missing the actual value, in which case you should use the maximum possible error as the absolute error. [2] If you know the actual value and the relative error, you can work backwards to find the absolute error.

Method 1
Method 1 of 3:

Using the Actual Value and Measured Value

PDF download Download Article
  1. The formula is , where equals the absolute error (the difference, or change, in the measured and actual value), equals the measured value, and equals the actual value. [3]
  2. The actual value should be given to you. If not, use a standardly accepted value. Substitute this value for .
    • For example, you might be measuring the length of a football field. You know that the actual, or accepted length of a professional American football field is 360 feet (including both end zones). So, you would use 360 as the actual value: .
    Advertisement
  3. This will be given to you, or you should make the measurement yourself. [4] Substitute this value for .
    • For example, if you measure the football field and find that it is 357 feet long, you would use 357 as the measured value: .
  4. Since absolute error is always positive, take the absolute value of this difference, ignoring any negative signs. This will give you the absolute error. [5]
    • For example, since , the absolute error of your measurement is 3 feet.
  5. Advertisement
Method 2
Method 2 of 3:

Using the Actual Value and Relative Error

PDF download Download Article
  1. The formula is , where equals the relative error (the ratio of the absolute error to the actual value), equals the measured value, and equals the actual value. [6]
  2. This will likely be a decimal. [7] Make sure you substitute it for .
    • For example, if you know that the relative error is .025, your formula will look like this: .
  3. This information should be given to you. Make sure you substitute this value for .
    • For example, if you know that the actual value is 360 ft, your formula will look like this: .
  4. This will cancel out the fraction.
    • For example:


  5. This will give you the value of , giving you the measured value.
    • For example:


  6. Since absolute error is always positive, take the absolute value of this difference, ignoring any negative signs. This will give you the absolute error. [8]
    • For example, if the measured value is 369 ft, and the actual value is 360 feet, you would subtract . So, the absolute error is 9 feet.
  7. Advertisement
Method 3
Method 3 of 3:

Using the Maximum Possible Error

PDF download Download Article
  1. This is the “to the nearest” value. This might be explicitly stated (for example, “The building was measured to the nearest foot.”), but it doesn’t have to be. To determine the measuring unit, just look at what place value the measurement is rounded to.
    • For example, if the measured length of a building is stated as 357 feet, you know that the building was measured to the nearest foot. So, the measuring unit is 1 foot.
  2. The maximum possible error is the unit of measure. [9] You might see it listed as a number.
    • For example, if the unit of measure is a foot, the maximum possible error is .5 ft. So you might see that the measurement of a building is . This means that the actual value of the building’s length could be .5 ft less or .5 ft more than the measured value. If it was any less/more, the measured value would have been 356 or 358 feet.
  3. [10] Since absolute error is always positive, take the absolute value of this difference, ignoring any negative signs. This will give you the absolute error.
    • For example, if you find the measurement of a building to be , the absolute error is .5 ft.
  4. Advertisement

Community Q&A

Search
Add New Question
  • Question
    How do I find absolute error of any equation?
    Donagan
    Top Answerer
    An equation does not contain an "absolute error." Re-read the introduction above.
  • Question
    How do I find the root value of a 6-digit number?
    Donagan
    Top Answerer
    If you're asking about square roots, see Calculate a Square Root by Hand .
  • Question
    What is the absolute error in 2.11?
    Donagan
    Top Answerer
    As explained above, the concept of "absolute error" involves both a measured value and an "actual" value.
See more answers
Ask a Question
      Advertisement

      Video

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Name
      Please provide your name and last initial
      Thanks for submitting a tip for review!
      Advertisement

      About This Article

      Article Summary X

      To calculate the absolute error, use the formula, “Absolute Error = Measured Value - Actual Value.” Begin by plugging the actual value into the formula, which will either be given to you or is the standardly accepted value. Then, make a measurement and put the measured value into the formula. Finally, subtract the actual value from the measure value to calculate the absolute error. If there are any negative signs, ignore them when you record your answer. To learn how to find the absolute error if you don’t have the measured value, keep reading.

      Did this summary help you?
      Thanks to all authors for creating a page that has been read 236,958 times.

      Reader Success Stories

      • Vishal Karmakar

        Aug 27, 2017

        "The examples clear it all up."
      Share your story

      Did this article help you?

      Advertisement