Percent error between an observed and a true value — with signed error and accuracy.
The true value goes in the second box — percent error is always measured against it, never against your own result. Keep the units the same in both boxes.
Percent error
How to use this tool
Type your measured result in the first box and the accepted or theoretical value in the second box — for example, 98 observed against a true 100. Use the same units in both.
The headline percent error is always positive. The signed error and signed percent error show the direction: negative means you measured low, positive means high.
Accuracy (100% minus percent error) and your result as a percentage of the true value are shown alongside, so a lab report can quote whichever form it needs.
Copy the percent error, absolute error and working for a lab report or homework answer.
Formula & worked example
Worked example: you measure 98 g, but the true value is 100 g. The percent error formula gives |98 − 100| ÷ |100| × 100 = 2 ÷ 100 × 100 = 2%. The signed error is 98 − 100 = −2, so the signed percent error is −2% — the minus sign tells you the measurement came in low. Accuracy is 100% − 2% = 98%. Another case: measuring 105 against a true 100 gives a 5% error, high.
Limitations — read this before you rely on it
Percent error is only as meaningful as the true value: if the accepted value itself is uncertain or rounded, a small percent error may be meaningless. It is also misleading for very small true values — an absolute error of 1 looks like a 100% error when the true value is 1, and an infinite error when it is 0 (which is why a true value of 0 is rejected here). Percent error says nothing about precision: repeated measurements can agree closely with each other while all being wrong by the same amount.
Frequently asked questions
Percent error measures how far a measured (observed) value is from the true (accepted) value, as a percentage of the true value. It is the standard way to report the accuracy of an experiment.
Percent error = |observed − true| ÷ |true| × 100. For 98 vs 100: |98 − 100| ÷ 100 × 100 = 2%. Always divide by the true value, not by your measurement — dividing by the observed value is the most common mistake.
Percent error itself is always positive, because it uses the absolute error. The signed percent error keeps the sign: negative means you measured low, positive means you measured high. This calculator shows both, so you get the size of the error and its direction.
It cannot be calculated when the true value is 0, because the formula divides by the true value. In that case report the absolute error instead (for example, 'off by 2 units'), which this calculator still shows if you can use a non-zero reference.
Percent error is about accuracy (closeness to the true value). Percent difference compares two measurements neither of which is the accepted truth, dividing by their average instead. Percent change compares a new value with an old one. Use this calculator when one value is known to be correct.