Table of Contents
What is Absolute and Relative Error?
Absolute Error is the difference between the true value and the measured value. Relative Error is the absolute error expressed as a percentage of the true value.
Define Absolute Error
The absolute error is the difference between the measured value and the actual value.
Absolute Error Formula
The absolute error is the difference between the measured value and the actual value. The absolute error is always positive.
Absolute Error Example
The absolute error is the difference between the true value and the estimated value.
For example, if you measure the length of a room and get a measurement of 10 feet, but the true length of the room is 12 feet, then the absolute error is 2 feet.
Classification Of Absolute Error
1. Absolute Error = Actual Value – Measured Value
2. Absolute Error = Difference Between The Actual Value And The Predicted Value
Relative Error Definition
A relative error is a measure of how close a measured value is to the true value. Relative error is expressed as a percentage of the true value.
Relative Error Formula
Relative error is a measure of the size of the error in a measurement relative to the size of the measurement itself. Relative error is always expressed as a percentage.
Relative Error Example
Sam measures the length of a room to be 10 feet. His friend, John, measures the same room to be 9 feet. The relative error in Sam’s measurement is 1/10 or 10%.
Relative Error as a Measure of Accuracy
The relative error is a measure of the accuracy of a measurement. It is defined as the absolute value of the difference between the measured value and the true value divided by the true value.
The relative error is always positive.
Absolute Error and Relative Error in Numerical Analysis
Absolute Error
- Absolute Error is defined as the difference between the true value and the estimated value.
- The absolute error is always positive.
Relative Error
- Relative Error is defined as the difference between the true value and the estimated value, divided by the true value.
- The relative error is always between 0 and 1.
Absolute and Relative Error Calculation – Examples
Absolute Error
The absolute error is the difference between the estimated and actual values.
absolute error = estimated value – actual value
Relative Error
The relative error is the absolute error divided by the actual value.
relative error = absolute error / actual value
