The percent error formula is used to determine the accuracy of a value measured or estimated compared to the actual or known value. It is often used in scientific experiments to understand the precision of results.
Here is the formula for calculating percent error:
Where:
- Experimental Value (or Measured Value) is the value you have obtained from your experiment or measurement.
- Actual Value (or True Value or Theoretical Value) is the value that is known through calculation or given as a standard, a known constant, or an accepted value.
To compute the percent error, follow these steps:
- Subtract the Actual Value from the Experimental Value.
- Take the absolute value of the step 1 result, which means you ignore any negative sign.
- Divide the absolute value from step 2 by the Actual Value to get the error ratio.
- Multiply the result from step 3 by 100 to convert it into a percentage.
The absolute value in this calculation means that the percent error will always be a positive number. This makes sense because percent error is a measure of how far off a measurement is, not in which direction.
Let’s work through an example:
Suppose you have conducted an experiment where you measured a value to be 45 grams, but the known standard value is 50 grams. The percent error would be calculated as follows:
- Experimental Value – Actual Value = 45 g – 50 g = -5 g
- Absolute Value = |-5 g| = 5 g
- Error Ratio = 5 g / 50 g = 0.1
- Percent Error = 0.1 × 100% = 10%
So, the percent error in this case would be 10%.