The **relative error calculator** is a tool used to determine the **relative error** of a measurement or calculation. **Relative error** is a measure of the **accuracy** of a measurement or calculation, and it is expressed as a **percentage** of the true or expected value.

Absolute Erroris the difference between the measured or calculated value and the true or expected value.True Valueis the actual or expected value.

## Relative Error Calculation Chart

Measured Value | True Value | Absolute Error | Relative Error |
---|---|---|---|

120.5 cm | 121 cm | 0.5 cm | 0.41% |

12.3 g | 12 g | 0.3 g | 2.5% |

85.2 mph | 84 mph | 1.2 mph | 1.43% |

45.67 kg | 45 kg | 0.67 kg | 1.49% |

19.8 liters | 20 liters | 0.2 liters | 1% |

## Relative Error Formula

The formula for calculating relative error is:

**Relative Error = (Absolute Error) / (True Value) x 100**

Let’s break down the formula and provide an example:

**Absolute Error**: The absolute error is the difference between the measured or calculated value and the true or expected value.

Example: If the measured value is12.3 gramsand the true value is12 grams, the absolute error is0.3 grams.

**True Value**: The true value is the actual or expected value against which the measured or calculated value is compared.

Example: In the previous example, the true value is12 grams.

**Relative Error**: The relative error is the absolute error expressed as a percentage of the true value.

Relative Error= (Absolute Error) / (True Value) x 100

In the example,Relative Error= (0.3 grams) / (12 grams) x 100 =2.5%

## How Do You Calculate Relative Error?

To calculate the **relative error**, you need to follow these steps:

**Identify the Measured Value**: This is the value you obtained through measurement or calculation.**Identify the True Value**: This is the actual or expected value against which the measured value is compared.**Calculate the Absolute Error**: The absolute error is the difference between the measured value and the true value.**Absolute Error**= |Measured Value – True Value|**Calculate the Relative Error**: The relative error is the absolute error expressed as a percentage of the true value.**Relative Error**= (Absolute Error) / (True Value) x 100

For example you need to measure the length of a table, and your measurement is **120.5 cm**. The true length of the table is **121 cm**.

Measured Value=120.5 cm

True Value=121 cm

Absolute Error= |120.5 cm – 121 cm| =0.5 cm

Relative Error= (0.5 cm) / (121 cm) x 100 =0.41%

The **relative error** of **0.41%** means that your measurement is within **0.41%** of the true value of **121 cm**, which gives you an idea of the **accuracy** of your measurement.