Enter your observed (experimental) value and true (theoretical) value to calculate the percentage error between them. You'll get the percent error, absolute error, and a breakdown of how far off your measurement is from the accepted value.
Percentage Error
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Absolute Error
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Relative Error (Decimal)
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Raw Difference (Observed − True)
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Percent error is a measure of how far off an observed or experimental value is from the true, accepted value. It expresses the discrepancy as a percentage of the true value, making it easy to compare errors across different scales of measurement.
Percentage error is calculated using the formula: % Error = (|Observed Value − True Value| / |True Value|) × 100. The absolute value is used so the result is always positive, representing the magnitude of the error regardless of direction.
Absolute error is simply the absolute difference between the observed and true value (|Observed − True|), expressed in the same units as the measurement. Percent error normalizes this by the true value and multiplies by 100, giving a unitless percentage that is easier to interpret across different contexts.
The standard percent error formula uses absolute values, so the result is always non-negative. However, some scientific contexts report a signed percent error to indicate whether the measurement was above or below the true value. This calculator returns the absolute (unsigned) percent error.
A small percent error indicates that the measured value is close to the true value, suggesting a high degree of accuracy. A large percent error means there is a significant discrepancy, which may point to measurement errors, flawed methodology, or instrument limitations.
What constitutes an acceptable percent error depends on the field and context. In many scientific experiments, a percent error below 5% is considered good, while highly precise fields like chemistry or physics may require errors below 1%. Engineering tolerances vary widely by application.
If the true value is zero, percent error cannot be calculated because the formula requires dividing by the true value, which would cause a division by zero. In such cases, alternative error metrics like absolute error or mean absolute deviation are used instead.
Percent error can arise from many sources including human measurement mistakes, instrument calibration issues, rounding during calculations, environmental factors, and the inherent limitations of the measuring device. Identifying the source helps improve experimental accuracy over time.