Relative Error Calculator

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.

1. To find out the absolute error, subtract the approximated value from the real one:

   |1.41421356237 - 1.41| = 0.00421356237

2. 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.

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:

• If you are weighing apples in a grocery store, and you are planning on buying 2 kg of apples, an absolute error of 1 kg can result in buying up to 50% more or less than you need. You wouldn't want to use such scales in a store, would you?
• When you weigh yourself at home, a 1 kg error makes a substantial difference - after all, you'd like to know whether you weigh 75 or 76 kg. Nevertheless, this error feels more acceptable than in the case of apples.
• However, if you want to weigh a 20-meter-long steel beam that weighs approximately 2 tonnes, you're not interested in a difference of one kilogram - it's a relative error of about 0.05%, which can easily be neglected.

As you can see, the bigger the real value, the higher the accepted absolute error.