Absolute and Relative Error – Concept, Formula and Solved Examples

# Absolute and Relative Error – Concept, Formula and Solved Examples

## 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.

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## 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

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