Percent error calculator

Percent error measures how close a calculated or observed value is to the true or accepted value. It is widely used in science, math, and engineering to evaluate the accuracy of measurements and predictions.

What Is Percent Error?

Percent error is the difference between an observed value and the true value, expressed as a percentage of the true value. This metric shows how far off a value is in comparison to the standard.

Formula for Percent Error:

\[
\text{Percent Error} = \left| \frac{\text{Observed Value} – \text{True Value}}{\text{True Value}} \right| \times 100
\]

Why Use Percent Error?

Percent error is useful because it provides a clear, standardized way to evaluate the accuracy of results. Instead of simply reporting the difference, the percent error shows the error size relative to the true value, making it easier to compare across different scenarios.

Steps to Calculate Percent Error

1. Identify the Observed and True Values: Determine the value you measured or calculated and the correct or accepted value.
2. Find the Difference: Subtract the true value from the observed value:
   \[
   \text{Difference} = \text{Observed Value} – \text{True Value}
   \]
3. Take the Absolute Value: Ignore negative signs to focus on the magnitude of the error:
   \[
   |\text{Difference}|
   \]
4. Divide by the True Value: Divide the difference by the true value to get the relative error.
5. Multiply by 100: Convert the relative error to a percentage by multiplying by 100.

Example of Percent Error Calculation

Let’s say you weigh an object, and your scale reads 10.5 kg, but the true weight is 10.0 kg:

1. Find the Difference:
   \[
   10.5 – 10.0 = 0.5
   \]
2. Divide by the True Value:
   \[
   0.5 \div 10.0 = 0.05
   \]
3. Convert to Percent:
   \[
   0.05 \times 100 = 5\%
   \]

The percent error is 5%.