How to calculate percent error

Calculating percent error is a common method in science and engineering to determine the accuracy of an experimental value compared to a known or accepted value. It’s a way to quantify how close an experimental result is to the actual value.

Here’s how you can calculate it:

Formula for Percent Error

The formula for calculating percent error is:

Steps to Calculate Percent Error

1. Identify the Accepted Value:
   • This is the value that is known or accepted as the true value. It might be a standard value or a value from literature.
2. Identify the Experimental Value:
   • This is the value you have obtained from your experiment or measurement.
3. Subtract the Accepted Value from the Experimental Value:
   • The difference might be positive or negative, but it will be converted to a positive value in the next step.
4. Take the Absolute Value of the Difference:
   • This ensures that the error is a non-negative number.
5. Divide the Absolute Difference by the Accepted Value:
   • This step computes the relative error in comparison to the accepted value.
6. Multiply by 100 to Convert to Percentage:
   • This gives you the percent error, showing the error as a percentage of the accepted value.

Example Calculation

Suppose you are performing an experiment where the accepted value of a quantity is 50.0 units, but your experimental value is 48.5 units. The percent error would be calculated as follows:

1. Difference between Experimental and Accepted Value:
   • 48.5−50.0=−1.5 units
2. Absolute Value of the Difference:
   • ∣−1.5∣ = 1.5 units
3. Dividing by the Accepted Value and Converting to Percentage:
   • (1.5 / 50.0) × 100% = 3%

So, the percent error in this case is 3%.

Tips

• Sign of Percent Error: Typically, the percent error is reported as a positive value, though in some contexts, keeping the sign (positive or negative) can indicate the direction of the error.
• Precision of Measurement: The percent error should reflect the precision of your measurements. For example, if your measurements are precise up to two decimal places, your percent error should also be rounded to two decimal places.
• Use in Context: Percent error is a useful tool for comparing experimental results to known values, but it’s important to consider the context and the precision of measurements when interpreting the result.