The % Error Formula: A Comprehensive Guide

What is the % Error Formula?

The % error formula is a statistical measurement that calculates the difference between an experimental value and a theoretical or expected value, expressed as a percentage of the theoretical value. It is commonly used in scientific and engineering applications to assess the accuracy and precision of measurements.

Formula and Calculation

The % error formula is given by:

``` % Error = (|Experimental Value - Theoretical Value| / Theoretical Value) x 100% ```

Where:

- % Error is the percentage error. - |Experimental Value - Theoretical Value| is the absolute value of the difference between the experimental value and the theoretical value. - Theoretical Value is the accepted or expected value.

Example

Suppose an experiment measures the mass of an object to be 102.5 grams, while the theoretical mass is 100 grams. Using the % error formula:

``` % Error = (|102.5 - 100| / 100) x 100% = 2.5% ```

This indicates that the experimental value has a 2.5% error compared to the theoretical value.

Applications

The % error formula has various applications, including:

- Evaluating the accuracy of experimental data. - Comparing different measurement techniques. - Determining the uncertainty in scientific measurements. - Assessing the reliability of sensors and instruments.

Limitations

While the % error formula is a useful tool, it has certain limitations:

- It does not take into account the sign of the error (positive or negative). - It can be misleading when the theoretical value is close to zero. - It assumes that the theoretical value is known with certainty, which may not always be the case.

Conclusion

The % error formula is a valuable tool for quantifying the accuracy and precision of measurements. It can help researchers, scientists, and engineers evaluate the reliability of their data and make informed decisions.