Absolute error

The absolute error is defined as the difference between the measured value and the exact value. It is a measure that shows how far or close a measurement is from the value it should have.

In this page we will show you how to calculate this type of error with the formula and we will also give you a calculator to obtain the absolute error automatically.




Definition of absolute error

As we said at the beginning, the absolute error is a magnitude determined by subtracting the value of a measurement taken minus the exact value it is supposed to have.

To make it clear, let's imagine that we have a 100-gram package of pasta but when we weigh it, it actually weighs 103 grams. There is a difference between the exact measurement it is supposed to have (100 g) and the one we obtain in the measurement (103 g).

This difference between the exact measurement and the one taken means that we have an absolute error that we will learn how to calculate in the next point.

Absolute error formula

Absolute Error formula

The formula for calculating the absolute error is as follows:

εa= x0 - x

Being:

  • X0: is the value of the measurement we have obtained.
  • X: is the exact or actual value that should have

For example, in the example we have seen in the previous point, the Ea would be calculated as follows:

εa= x0 - x = 103g - 100g = 3 grams

As you can see, the units of the absolute error are the same as those of measurement.

Another thing to keep in mind is that the absolute error is also can take negative values.

Difference between absolute error and relative error

Absolute error and relative error are often linked.. We already know what the former is and what it is used for, but how does it differ from relative error?

To calculate the relative error it is essential to have calculated the absolute error. . Once calculated, the relative error shows how large the absolute error is compared to the total size of the object we are measuring.

At the unit level, the absolute error carries the units of measurement, however, the absolute error is expressed as a fraction or percentage.

Continuing with the example of our packet of macaroni, we have already seen that εa was 3 grams. However, the relative error will be:

Relative Error = 3 / 100 * 100 = 3%

If you want to know more about the relative error and how it is calculated, we recommend you to click on the link we have just left.

Absolute error exercises

In case there are still doubts, let's see a solved exercise in which we are given a water jug with a capacity for 1 liter of water but which in our measurement has shown us that it has a capacity for 0.9 liters. What is the absolute error in this case?

We apply the formula we have seen in the theoretical point and we obtain that:

εa= x0 - x = 0.9 liters - 1 liter = -0.1 liters

As you can see, the difficulty involved is minimal, but if you have any doubts, leave us a comment and we will help you solve them.

Absolute error in Excel

Excel absolute error

Excel does not have any formula to calculate the absolute error, however, you can adapt one in a simple way since it is simply to apply a subtraction. For example, you can use this one:

=X-Y

You simply replace the value of X with the number of the measurement taken and the value of Y with the actual value it should have. When you press enter or accept the formula, Excel will automatically calculate the result.

Calculate absolute error online

If you want to get the error obsolute online and without formulas, you can use our online calculator that you will find at the top of the page.

We just need you to enter the values of the taken and the actual measurement. When you have done so, press the calculate button and the result will automatically appear on the screen.

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