Percent Error
Laboratory accuracy
Percent error compares a measured value with the theoretical expectation and indicates whether the method tends to overestimate or underestimate.
% Error = ((measured - theory) / theory) × 100
A negative sign indicates underestimation, while a positive sign indicates overestimation. For pure magnitude analysis, labs often use |% error|.
- Laboratory quality control
- Method comparison and validation
- Calibration performance assessment
Formulas
% Error = ((M - T)/T) × 100
M = T × (1 + %Error/100)
T = M / (1 + %Error/100)
Detailed examples
Example 1: Titration concentration
measured=0.196 mol/L; theory=0.200 mol/L
%Error=((0.196-0.200)/0.200)×100=-2.00%
measured=0.196 mol/L; theory=0.200 mol/L
%Error=((0.196-0.200)/0.200)×100=-2.00%
Example 2: Yield determination
measured=48.7 g; theory=50.0 g
%Error=-2.60%
measured=48.7 g; theory=50.0 g
%Error=-2.60%
Example 3: Predicted measured value
theory=10.00; %Error=-1.5%
M=10×(1-0.015)=9.85
theory=10.00; %Error=-1.5%
M=10×(1-0.015)=9.85
Interpretation
|%Error| < 1%: excellent, 1–5%: often acceptable, >5%: review setup, calibration, and sample handling.
|%Error| < 1%: excellent, 1–5%: often acceptable, >5%: review setup, calibration, and sample handling.
Technical Background
Systematic vs random error
Percent error mainly captures deviation from a reference value. Repeated measurements and standard deviation are needed to characterize random scatter separately.
Chemistry lab practice
Blank correction, instrument calibration, and certified reference materials are key tools to keep percent error low and results traceable.
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