Content

• To step
• Method 1 of 3: Using the actual value and the measured value
• Tips

The absolute error is the difference between the measured value and the actual value. It is one way to consider margins of error when measuring the accuracy of the values. If you know the actual and measured values, then the calculation of the absolute error is a simple subtraction. However, sometimes you do not know what the true value is, in which case you should consider the maximum possible error as the absolute error. If you know the actual value and the relative error, you can work backward to calculate the absolute error.

To step

Method 1 of 3: Using the actual value and the measured value

1. Draw up the formula for calculating the absolute error. The formula is ${ displaystyle Delta x = x_ {0} -x}$Plug the actual value into the formula. The actual value must be given. If not, use an acceptable default value. Substitute this value for ${ displaystyle x}$Determine the measured value. This is given, or you have to perform the measurement yourself. Substitute this value for ${ displaystyle x_ {0}}$Subtract the actual value from the measured value. Since the absolute error is always positive, take the absolute value of this difference and ignore any minus sign. This will give you the absolute error.
   • For example: because ${ displaystyle Delta x = -10}$Draw up the formula for the relative error. The formula is ${ displaystyle delta x = { frac {x_ {0} -x} {x}}}$Plug in the value for the relative error. This is probably a decimal. Make sure to substitute these for ${ displaystyle delta x}$Plug in the value for the actual value. This should be given. Substitute this value for ${ displaystyle x}$Multiply each side of the equation by the actual value. This will work out the fraction.
     • For instance:
       ${ displaystyle 0.025 = { frac {x_ {0} -100} {100}}}$Add the actual value to each side of the equation. This will give you the value of ${ displaystyle x_ {0}}$Subtract the actual value from the measured value. Since the absolute error is always positive, take the absolute value of this difference and ignore any minus signs. This will give you the absolute error.
       • For example, if the measured value is 104 meters and the actual value is 100 meters, then you calculate ${ displaystyle 104-100 = 4}$Determine which unit of measurement you are using. This is the value "accurate to the [unit]." This may have been stated explicitly (eg: "The building was measured to the centimeter"), but it does not have to be the case. Determine the unit of measure by looking at the number of decimal places to which the measurement was rounded.
         • For example: if the measured length of a building is given as 100 meters, then you know that the building has been measured to the nearest meter. So the unit of measure is the meter.
       • Determine the maximum margin of error. The maximum margin of error is ${ displaystyle { frac {1} {2}}}$Use the maximum margin of error as the absolute error. Since the absolute error is always positive, we take the absolute value of this difference and ignore any minus signs. This will give you the absolute error.
         • For example: if you measure that a building ${ displaystyle 90 +/- 0.0}$ meter, the absolute error is 0.5 meter.

Tips

• If the actual value is not given, you can look for the standard or theoretical value.