Calculate the percentage error between your experimental value and the theoretical (accepted) value with step-by-step working.
Percentage Error = |Experimental - Theoretical| / |Theoretical| × 100%
Where:
Absolute Error = |Experimental - Theoretical|
Relative Error = |Experimental - Theoretical| / |Theoretical|
Percentage error expresses how far a measured or estimated value is from a known true value, and it's more useful than a raw difference because it accounts for scale - being off by 5 units matters very differently depending on whether the true value is 10 (a 50% error) or 10,000 (a 0.05% error). Scientists use percentage error to evaluate the accuracy of experimental measurements against theoretical or accepted values, and quality control processes in manufacturing use it to determine whether a product's actual dimensions fall within acceptable tolerance. A classic example is calculating magnification percent error in microscopy or photography, where a lens or measurement tool's actual magnification is compared against its labeled or theoretical value.
Students in physics and chemistry labs report percentage error routinely as part of lab writeups, since it's a standardized way to communicate measurement accuracy that lets different experiments and different measured quantities be compared on the same relative scale.
These sound similar but measure different things - percentage error compares a measured value against a known true value, while percentage difference compares two values when neither is established as the "correct" one, which matters when choosing the right calculation for a given comparison.
Percentage error measures how accurate an experimental value is compared to the theoretical (accepted) value. It expresses the difference as a percentage of the theoretical value, making it easy to compare errors across different scales.
Absolute value ensures the error is always positive, regardless of whether the experimental value is higher or lower than the theoretical value. This focuses on the magnitude of the error rather than its direction.
Acceptable percentage error depends on the field and context. In physics experiments, errors under 5% are often considered good. In chemistry, 1-2% might be expected. In social sciences, larger errors may be acceptable. Always consider the context of your measurement.
Yes, percentage error can exceed 100% if the experimental value is more than double the theoretical value (or less than zero for positive theoretical values). This indicates a very large discrepancy between measured and expected values.
Percentage error is undefined when the theoretical value is zero because you cannot divide by zero. In such cases, use absolute error instead, or consider whether the measurement is meaningful when the expected value is zero.
Percentage error compares a measured value against a known true value, while percentage difference compares two values when neither is established as correct.
Percentage error accounts for scale, since being off by a fixed amount matters very differently depending on how large the true value actually is.
Scientists evaluating experimental accuracy and quality control processes in manufacturing both routinely use percentage error to assess measurement accuracy.
