Percent error formula
Percent error measures accuracy: %error = |experimental − theoretical| ÷ theoretical × 100. The absolute value keeps the result positive. To compare yield against a predicted maximum instead, use the percent yield calculator.
Dividing by the accepted value is what makes the figure comparable across experiments: an error of 0.01 means something very different when the true value is 9.81 than when it is 0.05.
How to use this calculator
Enter your measured (experimental) value and the accepted or theoretical value. The result is the percent error to two decimals — smaller is more accurate. Both values should be in the same units. For purity calculations see the mass percent calculator.
Putting the two values in the wrong fields is the usual mistake, since the accepted value has to be the denominator. Getting it backwards changes the answer whenever the two numbers differ noticeably.
Worked example
You measure gravity as 9.8 m/s² while the accepted value is 9.81 m/s². Percent error = |9.8 − 9.81| ÷ 9.81 × 100 = 0.10%, a very accurate result.
Interpret the number as a share of the true value: 0.10% means the reading is off by one part in a thousand. A large percent error points to a systematic problem — a miscalibrated instrument, an unaccounted-for variable, or a unit slip — rather than ordinary random scatter, which usually shows up as small variation between repeat readings instead. When neither value is the accepted one, the fairer comparison is a percent difference.
Frequently asked questions
- What is percent error?
- It is the size of the difference between an experimental value and the accepted value, expressed as a percentage of the accepted value.
- Why use absolute value?
- Percent error reports the magnitude of the deviation, so it is always positive regardless of whether you measured high or low.
- What is a good percent error?
- It depends on the experiment, but values under a few percent are generally considered accurate.
- Why must the accepted value not be zero?
- Dividing by zero is undefined, so percent error cannot be computed against a true value of zero.
- How is percent error different from percent difference?
- Percent error compares a measurement against a known correct value, so it measures accuracy. Percent difference compares two measurements when neither is the accepted one, and divides by their average instead.