Percent Error Calculator
Calculate percent error between accepted and experimental values. Includes absolute error, signed error, accuracy, and step-by-step solution.
Percent Error
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Formula Used
δ = |(100 − 95) ÷ 100| × 100%
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Percent Error
5%
Step-by-Step Calculation
Formula
δ = |vA − vE| ÷ |vA| × 100%
vA = 100 (accepted), vE = 95 (experimental)
Step 1: Calculate Absolute Error
|100 − 95| = 5
Step 2: Calculate Percent Error
(5 ÷ |100|) × 100% = 5%
Signed Error (Direction)
(95 − 100) ÷ |100| × 100% = 5% underestimate
Experimental Accuracy
95% accurate
Interpretation
Moderate error — review your measurement procedure. Consider recalibrating instruments or checking for systematic bias.
The negative signed error suggests your measurement was lower than the true value (systematic underestimation).
Percent Error Benchmarks
< 1%
Excellent
< 5%
Good
< 10%
Acceptable
> 15%
Needs Review
The Formula
Percent error measures how close an experimental value is to the accepted or theoretical value. The absolute value ensures the error is always positive — we care about the magnitude of the discrepancy, not the direction. In many lab contexts, a percent error under 5% is considered excellent, while over 15% indicates a procedural issue.
Variable Definitions
Accepted Value
The theoretical, true, or standard reference value. The expected result in a perfect experiment.
Experimental Value
The measured or observed value from your experiment. What you actually got.
Percent Error
The absolute difference between accepted and experimental values, divided by the accepted value, times 100%. Always expressed as a positive percentage.
Experimental Accuracy
100% minus the percent error. Represents how close the experimental value is to the truth on a percentage scale.
Relative Error
The absolute error divided by the accepted value. The decimal form of percent error before multiplying by 100.
How to Use This Calculator
- 1
Enter the accepted/true value (the theoretical or standard reference).
- 2
Enter the experimental/observed value (what you actually measured in your experiment).
- 3
Review the percent error, absolute error, accuracy, and relative error.
- 4
Check the signed error to see if you overestimated (positive) or underestimated (negative) the true value.
- 5
Use the accuracy percentage to quickly assess experimental quality: >95% is excellent, <85% warrants investigation.
Percent error measures the distance between an experimental measurement and the accepted true value.
Understanding the Concept
Percent error is a staple of chemistry and physics lab work. It quantifies the accuracy of experimental measurements by comparing them to a known standard. The absolute value in the formula ensures that overestimates and underestimates are treated equally — the magnitude of the error is typically more important than the direction when assessing experimental technique. However, the signed error is also crucial for diagnosing systematic bias: if all your measurements are consistently above or below the true value, you likely have a calibration or procedural issue that should be corrected. Random variation, on the other hand, produces a mix of positive and negative signed errors and is reduced by taking more measurements and averaging. Percent error differs from percent difference, which compares two experimental values when neither is known to be correct. A common question in lab classes: "I got 15% error — is that good?" The answer depends on the context. In introductory physics labs, under 5% is excellent, 5-15% is acceptable, and over 15% suggests a problem worth investigating. In advanced analytical chemistry, errors under 1% are expected.
Frequently Asked Questions
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