About Percent Error

Percent error is a measure of how inaccurate a measurement is, standardized to how large the measurement is. It is the relative error expressed as a percentage.

Formula

The formula for calculating percent error is:

Where:

• Observed Value: The value you measured or calculated
• True Value: The accepted or known value
• | |: Absolute value (always positive)

Examples

Example 1: If the true value is 10 and you measured 9, the percent error is:

Percent Error = |9 - 10| / |10| × 100% = 1/10 × 100% = 10%

Example 2: If the true value is 50 and you measured 55, the percent error is:

Percent Error = |55 - 50| / |50| × 100% = 5/50 × 100% = 10%

Applications

• Science: Evaluating the accuracy of experimental measurements
• Engineering: Assessing the precision of calculations and designs
• Quality Control: Determining if products meet specifications
• Education: Teaching students about measurement accuracy

Interpreting Percent Error

• Low percent error (0-5%): Indicates high accuracy
• Moderate percent error (5-10%): Acceptable for many applications
• High percent error (>10%): May indicate problems with measurement technique or equipment