Understanding Percentage Error
Percentage error measures the accuracy of a measurement or estimate compared to a known or expected value. It's widely used in science, engineering, and quality control.
Formula
Percentage Error = (|Actual - Expected| / Expected) x 100
Key Points
- Always uses absolute value (always positive)
- Shows relative magnitude of error
- Lower percentage = more accurate
- 0% = perfect accuracy
Examples
Example 1: Measured 9.8m but expected 10m
Error = (|9.8 - 10| / 10) x 100 = 2%
Example 2: Estimated 150 but actual was 140
Error = (|150 - 140| / 140) x 100 = 7.14%
Applications
- Scientific experiments
- Manufacturing tolerances
- Financial forecasting
- Quality assurance
- Statistical analysis
- Academic lab reports
Interpreting Results
0-5%: Excellent accuracy | 5-10%: Good accuracy | 10-20%: Fair accuracy | 20%+: Poor accuracy (context dependent)
Common Causes of Error
Measurement limitations, human error, environmental factors, equipment calibration, and theoretical assumptions.
Quick Tips
- Double-check your inputs for accurate results
- Use parentheses to clarify order of operations
- Results are rounded — consider significant figures
Frequently Asked Questions
It's the relative difference between an actual and expected value, expressed as a percentage.
Divide the absolute difference by the expected value, multiply by 100.
To make error always positive, focusing on magnitude not direction.
Generally under 5% is excellent, but it depends on context.
No, it uses absolute value so it's always positive.
Percentage error uses the expected value as reference, not the average.