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 quantifies how far a measured or estimated value deviates from a known true or accepted value, expressed as a percentage of that true value, making it useful for comparing measurement accuracy across different scales — a 5-unit error means something very different when measuring a quantity around 10 versus a quantity around 10,000, and percentage error normalizes for this scale difference in a way a raw error amount can't.
This calculation is widely used in scientific experiments to evaluate how closely experimental results match theoretical predictions, in manufacturing quality control to assess how far a produced item's dimensions deviate from specification, and in forecasting to evaluate how accurate a prediction turned out to be compared to the actual observed outcome.
Percentage error specifically requires knowing a true or accepted reference value to compare against, while percentage difference compares two values without either one being designated as objectively "correct" — a subtle but important distinction, since percentage error implies one value is the standard being measured against, while percentage difference treats both values more symmetrically without assuming either represents ground truth.
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.
Enter 599.43 nm as your experimental value along with the accepted true value above, and the calculator instantly returns the percentage error between them.
There's no fixed threshold - percentage error is simply the difference between an assumed or measured value and the true value, expressed as a percentage. Enter both values above to calculate the exact percentage error.
