What is the Difference Between Absolute Error and Relative Error?
🆚 Go to Comparative Table 🆚The difference between absolute error and relative error lies in the way they express the error in a measured value. Here are the key differences between the two:
- Absolute Error: This is the difference between the actual value and the measured value of a quantity. It gives the magnitude of the error without considering the magnitude of the actual value. The formula for absolute error is: $$|x0 - x|$$, where $$x0$$ is the actual value and $$x$$ is the measured value.
- Relative Error: This is the ratio of the absolute error of a measurement and the actual value of the quantity. It gives the magnitude of the error relative to the actual value. The formula for relative error is: $$\frac{|x0 - x|}{x0}$$, where $$x_0$$ is the actual value and $$x$$ is the measured value. Relative error is usually expressed as a percentage by multiplying the fractional error by 100.
In summary, absolute error represents the actual difference between the measured and true values, while relative error represents the difference between the measured and true values relative to the true value itself. Absolute error is a measure of the accuracy of a measurement, while relative error is a measure of the precision of a measurement.
Comparative Table: Absolute Error vs Relative Error
The main difference between absolute error and relative error lies in how they are calculated and the information they provide about the measurement. Here is a table comparing the two:
Feature | Absolute Error | Relative Error |
---|---|---|
Definition | The difference between the actual value and the measured value of a quantity. | The proportion of the absolute error relative to the measured value. |
Formula | $$\text{Absolute error} = | \text{measured value} - \text{true value} |
Unit of Measurement | The unit of measurement of the quantity being measured, e.g., centimeters, grams, etc. | A proportion or percentage, indicating the relationship between the error and the measured value. |
Application | Absolute error is useful for determining the accuracy of a measurement and is typically expressed in the same unit as the measured value. | Relative error is useful for comparing the error of different measurements, even if their units are different, as it is expressed as a proportion or percentage. |
For example, consider a carpenter measuring wooden floorboards with a tape measure that has an absolute error of 0.5 inches. The carpenter measures one board with the tape and finds that it is 36 inches long. The absolute error of this measurement is 0.5 inches. The relative error of the measurement is $$\frac{0.5}{36} = 0.014$$ or 1.4%.
- Absolute vs Relative
- an Absolute vs a Relative URL
- Absolute vs Relative Humidity
- Relative vs Absolute Dating
- Random Error vs Systematic Error
- Accuracy vs Precision
- Exception vs Error
- Absolute vs Relative Refractory Period
- Error vs Mistake
- Absolutism vs Relativism
- Absolute vs Comparative Advantage
- Velocity vs Relative Velocity
- Exact vs Accurate
- Frequency vs Relative Frequency
- Relativity vs Special Relativity
- Reliability vs Validity
- Absolute vs Relative Configuration in Stereochemistry
- Normality Factor vs Titration Error
- Absolute Cost Advantage vs Comparative Cost Advantage