Everyday math
Calculate percentage error by comparing an observed value with an accepted reference value.
Enter your numbers to see the answer.
Percentage Error Calculator guide
Percentage error tells you how far a measured or observed value strays from a value you trust, expressed relative to that trusted figure. Enter the accepted value (the textbook constant, the calibrated reference, the manufacturer specification, or the forecast) and the observed value you obtained, and the calculator divides the absolute gap by the accepted value. It is the standard check in school labs, quality control, and forecasting, where the question is “how wrong was I”, not “how much did it change”. The accepted value is always the denominator, which separates this tool from the percentage difference calculator (which divides by the average of two peers) and from percentage increase or decrease (which divide by an earlier value). The result is reported as a positive number, so a reading of 96 against 100 and a reading of 104 against 100 both show 4% error.
Percentage error (%) = |observed − accepted| ÷ |accepted| × 100.
Worked example with the defaults: accepted value 100, observed value 96. The absolute error is |96 − 100| = 4. Divide by the accepted value: 4 ÷ 100 = 0.04. Multiply by 100 and the percentage error is 4%, which the calculator displays as “4% error” with rows for the absolute error (4) and the accepted value (100). An observed value of 104 would give the same 4% because the sign of the error is dropped.
Both values must be in the same unit; the unit cancels in the division. Enter plain numbers without % signs. The result is relative to the accepted value only, so the same absolute error of 4 is a 4% error against 100 but a 40% error against 10. The display rounds to two decimals by default.
The result follows directly from the numbers you entered, so its accuracy is the accuracy of those inputs. The most common source of a surprising answer is a mismatch between the question you meant to ask and the one the calculator answered, so re-read the field labels if the figure looks wrong. The formula is shown above so you can check the arithmetic yourself. On this page the figure rests entirely on accepted value and observed value, so start there if the percentage error calculator returns something you did not expect.
Good to know: putting the observed value in the accepted field changes the denominator and therefore the answer (4 ÷ 96 gives 4.17%, not 4%). Percentage error is not the same as the percentage difference between two measurements; that uses the average. An accepted value of zero cannot be used, because dividing by zero is undefined; the tool returns 0% in that case rather than a meaningful figure.
Results are planning estimates. Check the units, product coverage, carrier rules, or local rates before making a purchase or financial decision.
How it works
Calculate percentage error by comparing an observed value with an accepted reference value. This tool explains the calculation so you can adjust the assumptions to match your situation.
Worked example
With Accepted value = 100 · Observed value = 96 → 4 % error (absolute percentage error). Change an input above and this example updates with your numbers.
Common questions
4%. The absolute error is 4, and 4 ÷ 100 × 100 = 4%. A measurement of 104 gives the same 4% because the calculator reports the size of the error, not its direction.
Subtract the accepted value from your measured value, take the absolute value, divide by the accepted value, and multiply by 100. The accepted value comes from a reference table, a calibrated standard, or the theoretical result.
No. Percent error divides by a known accepted value; percent difference divides by the average of two values when neither is the reference. For 96 and 100, the error is 4% but the percentage difference is 4.08%.
This calculator always shows a positive figure because it uses the absolute error. Some courses keep the sign to show whether a reading was high or low; if yours does, note that 96 against 100 would be −4%.
It depends on the field. School experiments often accept under 5%, calibrated instruments may need under 1%, and rough forecasts tolerate 10% or more. Compare your result with the tolerance specified for the task rather than a universal rule.