Percentage Error Calculator — Measure Accuracy Instantly
Calculate the percentage error between a measured value and an accepted value. For percentage difference, try our percentage difference calculator.
Table of Contents
Calculate Percentage Error
Enter the measured (experimental) value and the accepted (true) value.
Percentage Error – Complete Explanation
Percentage error measures how inaccurate a measurement is, as a percentage of the accepted (true) value.
Percentage Error Formula
% Error = |Measured - Accepted| / |Accepted| × 100
1. What Is Percentage Error?
It answers: "How close did my measurement come to the true value?"
- Always positive — uses absolute value.
- Referenced to accepted value — denominator is the true value.
- Measures accuracy — not precision.
2. The Formula Explained
- |Measured - Accepted|: Absolute error.
- |Accepted|: Reference point (true value).
- × 100: Convert to percentage.
3. Step-by-Step Examples
3.1 Example 1: Measuring Gravity
Measured g = 9.6 m/s², Accepted g = 9.8 m/s² |9.6 - 9.8| = 0.2 0.2 / 9.8 = 0.0204 × 100 = 2.04%
3.2 Example 2: Overestimated Measurement
Measured boiling point = 102°C, Accepted = 100°C |102 - 100| = 2 2 / 100 = 0.02 × 100 = 2%
4. More Examples
48 vs 50 → 4% error
103 vs 100 → 3% error
19.5 vs 20.0 → 2.5% error
100 vs 100 → 0% error (perfect)
5. Absolute Error vs. Relative Error
Absolute Error: |Measured - Accepted| — same units as measurement.
Relative Error: Absolute Error / |Accepted| — dimensionless ratio.
Percentage Error: Relative Error × 100 — percentage form.
6. Percentage Error vs. Percentage Difference
Error: Denominator = accepted value. Use when you have a "true" value.
Difference: Denominator = average. Use when comparing two values equally.
7. Systematic vs. Random Errors
Systematic: Consistent, repeatable, one-directional (faulty equipment).
Random: Unpredictable scatter around true value (human reaction time).
8. Common Mistakes to Avoid
- Using measured value as denominator — must use accepted value.
- Forgetting absolute value
- Confusing with percentage difference
- Dividing by zero — accepted value cannot be zero.
9. Real-World Applications
- Physics/Chemistry labs
- Engineering tolerances
- Quality control
- Forecasting accuracy
10. Practice Problems with Solutions
0.97 vs 1.00 → 3% error
24.3 vs 25.0 → 2.8% error
11. Tips for Mastering Error Analysis
- Identify accepted value first.
- Track units — absolute error has same units as measurement.
- Report both absolute and percentage error.
12. Final Thoughts
Percentage error bridges raw measurements and meaningful accuracy assessment. Use this calculator to verify your work, but practice manually to build confidence.
13. Frequently Asked Questions
The accepted value is the "truth" — the reference point. Dividing by it expresses the error as a fraction of what the measurement should be. This normalizes the error, making it comparable across different scales. An error of 1 unit means very different things depending on whether the true value is 2 or 1000.
No. The formula uses the absolute value |Measured - Accepted|, so the result is always non-negative. The direction of the error (over or under) is reported separately. Percentage error represents the magnitude of the inaccuracy, not its direction.
Percentage error is undefined when the accepted value is zero because division by zero is undefined. This is a common issue when the true value is zero (e.g., measuring a zero baseline). In such cases, use absolute error instead of percentage error to describe accuracy.
Percentage error divides by the accepted (true) value. Percentage difference divides by the average of the two values. Use error when you have a known correct answer to compare against. Use difference when neither value is the "true" one — just comparing two numbers symmetrically.
It depends on the application. In physics labs, under 5% is generally good, under 1% is excellent. In engineering, tolerances may require less than 0.1%. In some fields, 10-20% may be acceptable. The context determines what counts as "good" accuracy.
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Conclusion
Percentage error bridges raw measurements and meaningful accuracy assessment. Use this calculator to verify your work, but practice manually to build confidence.
Readers who wish to continue practicing and reinforce what they've learned can explore the companion learning resource for guided exercises.