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Percent Error
6.00
%
Good Accuracy
What Is Percent Error?
Percent error (also called percentage error) measures how far an observed (measured or experimental) value deviates from the true (accepted or theoretical) value, expressed as a percentage. It is used in science, engineering, and statistics to quantify measurement accuracy.
The Percent Error Formula
Standard (unsigned):
Percent Error = |Observed − True| / |True| × 100
Signed (shows direction):
Signed % Error = (Observed − True) / True × 100
Positive = overestimation
Negative = underestimation
Related:
Absolute Error = |Observed − True|
Relative Error = |Observed − True| / |True|
Accuracy = 100 − Percent Error (%)
Interpreting Percent Error
What counts as a "good" percent error depends on the field. In chemistry lab experiments, <5% is generally acceptable. In physics, <1% may be expected for precision instruments. In engineering, tolerance varies by application — structural tolerances might allow ±10%, while machined parts might require <0.1%.
What causes percent error in experiments?
Common sources of percent error: measurement instrument precision limits, parallax reading errors, environmental factors (temperature, pressure fluctuations), human reaction time (e.g. timing experiments), impure materials or wrong concentrations, systematic bias in equipment calibration, and rounding during calculation. Errors fall into two categories: random errors (which average out over repeated trials) and systematic errors (which consistently skew results in one direction).
Why do we use absolute value in the percent error formula?
The absolute value ensures percent error is always a non-negative number representing the magnitude of deviation regardless of direction. When we say a measurement has "5% error," we mean it deviates by 5% — not whether it's too high or too low. For directional analysis (whether you over- or underestimated), use the signed percent error formula instead.
What if the true value is zero?
Percent error is undefined when the true value is zero, because you cannot divide by zero. In such cases, use absolute error instead. Alternatively, if comparing near-zero values, use the percent difference formula (which divides by the average of both values rather than one specific value as the denominator).
