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The relative error is the ratio of the absolute error of a measurement to the exact value. The relative error tells how good a measurement is relative to the size of the object being measured. In other words, the relative error indicates how significant the absolute error is.
Relative Error =Absolute Error/Exact Value
The Relative Error Formula can be rewritten by substituting the Absolute Error Formula.
Relative Error =|Measured Value-Exact Value|/Exact Value
The percent error is the product between the relative error and 100 %. It represents the relative error as a percentage.
Percent Error = Relative Error * 100 %
Consider, for example, a person fishing who expected to catch 480 crayfish. However, the number of crayfish they ultimately caught was 400. The percent error explains the degree of the mistake in the person's estimation.
| Absolute Error | Relative Error | Percent Error |
|---|---|---|
| |480- 400| = 80 | 80/400 = 0.2 | 0.2* 100 % = 20 % |
The absolute error only says that the fisher was wrong by 80 crayfish. In contrast, the percent error says that the estimation was wrong by 20 %, which is more significant information for future predictions.