Relative error measures the size of the absolute error in relation to the true or accepted value, usually expressed as a percentage. It provides context for understanding how large the error is compared to the correct value. Percent error is another name for relative error when the result is expressed as a percentage.
The formula for relative error is:
Relative Error = |Measured value – True value| / True value
This formula calculates the absolute difference between the measured or estimated value and the true value, divided by the true value. In other words, it is the absolute error divided by the true value. The result is often multiplied by 100 to express it as a percentage. Relative error is useful because it provides a sense of how large the error is in proportion to the correct value, making it easier to compare errors across different scales or units.
For example, if you estimate a building’s height as 98 meters when its actual height is 100 meters, the relative error is:
(100 – 98) / 100 = 0.02 or 2%
The estimate is off by 2%.
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