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 Error is the difference between the measured or calculated value and the true or expected value.
- True Value is 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 100Let’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 is 12.3 grams and the true value is 12 grams, the absolute error is 0.3 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 is 12 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.