Percent Error Calculator
Calculate the percentage error between an observed (measured) value and a theoretical (true) value. Essential for science labs and quality control.
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Error Analysis Results
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accuracy measure
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|Observed - True|
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decimal form
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quality assessment
💡 Note: Percent error is always expressed as a positive value (absolute value). It tells you how far off your measurement is from the true value, as a percentage.
What is Percent Error?
Percent error is the difference between an approximate (measured) value and an exact (known) value, expressed as a percentage of the exact value. It is widely used in science and engineering to report the accuracy of experimental measurements.
The Percent Error Formula
Percent Error = (|Observed - Theoretical| / |Theoretical|) × 100%
Where:
| | denotes the absolute value (always positive)
Where:
| | denotes the absolute value (always positive)
Step-by-Step Example
You measure the acceleration due to gravity as 9.8 m/s², but the accepted value is 9.81 m/s².
- Find the difference: 9.8 - 9.81 = -0.01
- Take the absolute value: |-0.01| = 0.01
- Divide by the true value: 0.01 / 9.81 ≈ 0.00102
- Multiply by 100: 0.00102 × 100 = 0.102%
The percent error is 0.102%, which is extremely accurate!
Percent Error vs. Percent Difference
| Metric | Formula Purpose | When to Use |
|---|---|---|
| Percent Error | Compare measured value to a known true value | Lab experiments, quality control |
| Percent Difference | Compare two measured values (neither is "true") | Comparing two experimental results |
| Percent Change | Compare a new value to an old value | Finance, growth rates, inflation |
What is a "Good" Percent Error?
- < 1%: Excellent accuracy. Common in high-precision physics labs.
- 1% - 5%: Good accuracy. Acceptable for most high school and college labs.
- 5% - 10%: Fair accuracy. May indicate minor systematic errors.
- > 10%: Poor accuracy. Likely indicates a flaw in the experimental method or equipment.
⚠️ Important: If the theoretical (true) value is 0, percent error cannot be calculated because division by zero is undefined. In such cases, use Absolute Error instead.
Sources of Error in Experiments
- Human Error: Misreading instruments, calculation mistakes.
- Instrumental Error: Equipment not calibrated correctly.
- Environmental Error: Temperature, humidity, or pressure affecting results.
- Systematic Error: Consistent bias in one direction (e.g., a scale that always reads 0.1g too high).
- Random Error: Unpredictable fluctuations in readings.
References
- ThoughtCo. "How to Calculate Percent Error." 2026.
- Science Buddies. "Error Analysis." 2026.