You can use our relative error calculator to estimate both the absolute and relative error for any measurement or calculation. Let's analyse the difference between these two types of error with an example.
Let's say you want to determine the value of the square root of two. The value you find online is 1.41421356237, but you wonder how accurate it would be to simply write it rounded to two significant figures. Note, that this is different to decimal points - see the significant figures calculator for more information.
To find out the absolute error, subtract the approximated value from the real one:
|1.41421356237 - 1.41| = 0.00421356237
Divide this value by the real value to obtain the relative error:
|0.00421356237 / 1.41421356237| = 0.298%
As you can see, the relative error is lower than 1%. In many cases, this is considered a good approximation.
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The main advantage of the relative error is that, since it can only take values between 0-100%, it's easy to evaluate whether an error is big or small. It's much more challenging to determine whether a specific absolute error is of sufficient accuracy. For example, let's imagine you take measurements of weight with an absolute error of 1 kg:
As you can see, the bigger the real value, the higher the accepted absolute error.
The absolute error also called the approximation error, is the absolute value of the difference between the actual value and the measured value. The absolute error formula is
absolute error = |actual value - measured value|
The actual value is otherwise known as the real or true value. On the other hand, the measured valueis an approximation.
Relative error (or percent error), on the other hand, expresses the error in terms of a percentage. You can use the following relative error formula:
relative error = |absolute error / actual value| = |(actual value - measured value) / actual value|
We typically express both the absolute and relative errors as positive values, hence the use of absolute values.
The absolute error is the discrepancy between your measurement and the true value, while the relative error is the ratio between the absolute error and the absolute value of the true value.
The relative error helps us asses how accurate the measured value is when compared to the true value.
Relative error is known under several different names:
The answer is 0.05 or 5%. To arrive at this result, we apply the relative error formula:
relative error = |(actual - measured) / actual|.
actual = 40 and
measured = 42, we obtain
relative error = |(42-40) / 40| = 1/20 = 0.05.
Bertrand's paradox is an intriguing warning for every scientist: dealing with infinity and randomness can lead to pitfalls!