Calculate The Percentage Error in F and N

The percentage error is a measure of the accuracy of a measured or calculated value compared to the true value. It helps quantify how much your observed value (f) differs from the actual value (n) in percentage terms.

What is percentage error?

Percentage error is a common metric used in science, engineering, and data analysis to assess the accuracy of measurements or calculations. It provides a standardized way to compare how close an observed value is to the true value, expressed as a percentage.

In scientific experiments, percentage error helps determine if a measurement is within acceptable limits. In financial calculations, it might indicate the deviation of an estimate from the actual value. In statistical analysis, it helps evaluate the precision of models.

Formula for percentage error

The percentage error is calculated using this formula:

Percentage Error = |(f - n) / n| × 100%

Where:

f = observed or measured value
n = true or accepted value

The absolute value ensures the result is always positive, regardless of whether f is higher or lower than n.

How to calculate percentage error

To calculate the percentage error:

Identify the observed value (f) and the true value (n)
Subtract the true value from the observed value (f - n)
Divide the result by the true value (f - n)/n
Take the absolute value of the result to ensure positivity
Multiply by 100 to convert to a percentage

For example, if you measure a length as 9.5 cm when the true length is 10 cm:

Percentage Error = |(9.5 - 10) / 10| × 100% = 5%

This means your measurement was 5% lower than the true value.

Interpreting percentage error

The percentage error helps you understand:

How accurate your measurements or calculations are
Whether your results are within acceptable tolerances
Which factors might be causing discrepancies

Common interpretations:

Percentage Error Range	Interpretation
0% - 5%	Excellent accuracy, typically within acceptable limits
5% - 10%	Good accuracy, but may need improvement
10% - 20%	Moderate accuracy, may need calibration or verification
20%+	Poor accuracy, significant discrepancies may exist

Lower percentage errors indicate more accurate measurements or calculations. However, what constitutes an acceptable error depends on the specific application and context.

FAQ

What is the difference between percentage error and absolute error?: Absolute error is simply the difference between observed and true values (f - n), while percentage error expresses this difference as a percentage of the true value.
When should I use percentage error instead of absolute error?: Use percentage error when comparing results across different scales or when you need to express the error in relative terms. Absolute error is more appropriate when comparing measurements of the same scale.
Can percentage error be negative?: No, percentage error is always expressed as a positive value because we take the absolute value of the calculation.
What if the true value (n) is zero?: The formula would be undefined (division by zero). In such cases, you should use absolute error instead or reconsider your measurement approach.