Percent Error Calculator – Measurement Accuracy
Calculate percent error between experimental and theoretical values.
About This Calculator
Calculate percent error between experimental and theoretical values. Use the calculator above for instant results.
Understanding Percent Error
Percent error measures the size of a measurement error relative to an accepted or theoretical value. The subtraction finds the absolute error, while division by the accepted value puts that error in context. A difference of 0.2 units can be tiny when the reference is 1000, but very large when the reference is 0.5.
The absolute-value bars matter because percent error normally reports magnitude, not direction. If direction matters, keep the sign separately as a signed relative error: a positive signed error indicates an overestimate and a negative one indicates an underestimate. The denominator is the accepted value, not the experimental value. Changing the denominator changes the question being answered.
Percent error is also different from percent difference. Percent error is appropriate when one value is treated as the reference. Percent difference is used when two measured values have equal status and commonly divides their absolute difference by their average. If the accepted value is zero, the usual percent-error formula is undefined because division by zero has no meaning; report absolute error or use a context-appropriate alternative instead.
Interpret the result in context rather than treating one percentage as universally good or bad. Measurement uncertainty, instrument resolution, calibration, sampling, and the requirements of the experiment determine whether an error is acceptable. A small percent error indicates closeness to the reference value, but it does not by itself prove that a method is unbiased or precise.
Worked Examples
- |9.75-9.81|/9.81 x 100 = 0.61%
Answer: 0.61% error
- |4.2-4.0|/4.0 x 100 = 5.0%
Answer: 5.0% error
- 1.8% error
Answer: 1.8% error
Experimental value = 49.2, accepted value = 50.0.
- |49.2 − 50.0| / 50.0 × 100 = 1.6%
Answer: 1.6% error
The signed error is negative, so the measurement is an underestimate even though percent error is reported as positive.
Experimental value = 0.102, accepted value = 0.100.
- |0.102 − 0.100| / 0.100 × 100 = 2.0%
Answer: 2.0% error
A difference of only 0.002 still represents 2% because the reference value itself is small.
Who Uses This Calculator?
Evaluate measurement accuracy.
Lab reports.
Quality control.
Measurement system analysis.
Common Mistakes to Avoid
❌ Forgetting absolute value
% error is always positive — it measures magnitude not direction.
❌ % error vs % difference
Error: vs true value. Difference: between two experimental values.
❌ Dividing by the measured value
For percent error, divide by the accepted or theoretical value. Dividing by the experimental value produces a different relative quantity and can noticeably change the percentage.
❌ Treating zero as an ordinary reference
The standard formula is undefined when the accepted value is zero. Use absolute error or another metric suited to the experiment instead of forcing a percentage.
Frequently Asked Questions
Formula?
|experimental - theoretical| / |theoretical| x 100%.
Acceptable error?
There is no universal acceptable percent error. Use the tolerance, uncertainty, and quality requirements for your specific experiment or method.
Systematic vs random?
Systematic: consistent bias. Random: unpredictable variation.
Can percent error be greater than 100%?
Yes. If the absolute error is larger than the magnitude of the accepted value, percent error exceeds 100%. For example, measuring 25 when the accepted value is 10 gives |25 − 10|/10 × 100 = 150%.
Does a low percent error mean high precision?
Not necessarily. Low percent error describes accuracy relative to a reference. Precision describes how closely repeated measurements agree with one another. A set of measurements can be tightly clustered but consistently biased, giving high precision and poor accuracy.
Should units appear in percent error?
No. The numerator and denominator have the same units, so the units cancel. The final value is dimensionless and is expressed as a percentage. Convert measurements to compatible units before subtracting them.
When should I use percent difference instead?
Use percent difference when comparing two experimental values and neither is designated as the accepted reference. A common formula is |A − B| divided by the average of |A| and |B|, multiplied by 100%.
Formula Explorer connections
Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.