Percent Error Calculator
Enter the observed value, the one you measured, and the true value, the accepted or theoretical one. Press Calculate. The calculator divides the gap between them by the size of the true value and shows the percent error as a positive number, then the signed error, which says whether the reading came in low or high. The true value cannot be 0. To compare two measurements when neither is the reference, switch to Percent Difference. Results are rounded to 4 decimal places.
How to use the Percent Error Calculator
- Enter your numbers in the Percent Error Calculator above.
- Press the Calculate button to see the result.
- To try other numbers, change any value and press the button again.
The percent error formula
Percent error = |Observed − True| / |True| × 100 · · · Signed = (Observed − True) / |True| × 100 · · · Percent difference = |A − B| / ((|A| + |B|) / 2) × 100
Take the difference between the observed and the true value, ignore its sign, divide by the size of the true value and multiply by 100. The calculator works from the numbers exactly as you type them and rounds once, at the end. Without the absolute value bars on top you get the signed error, which is negative when the observed value is low. Percent difference divides the gap by the average size of the two values, so swapping them gives the same answer.
Worked example
A lab measures gravity at 9.7 m/s². The accepted value is 9.81 m/s². Percent error = |9.7 − 9.81| / 9.81 × 100 = 0.11 / 9.81 × 100, which the calculator shows as 1.1213%. The measurement came in low, so the signed error is −1.1213%. For the percent difference between two readings of 12 and 15, the gap is 3 and their average is 13.5, so the calculator shows 3 / 13.5 × 100 = 22.2222%.
Frequently asked questions
What is an acceptable percent error?
There is no single cutoff. Your course, lab manual or product specification sets the limit, so look it up there and compare it with the figure the calculator shows.
When should I use signed vs. absolute error?
Use the absolute error when only the size of the miss matters. Use the signed error when the direction matters, for example to spot an instrument that always reads high. This calculator shows both. If your observed value is below the true value, the signed error is negative, and that holds for a negative true value too: −5 against −4 gives −25%, because −5 is below −4.
How is this different from percent difference?
Percent error compares a measurement with an accepted value. Percent difference compares two measurements when neither one is the reference: |A − B| / ((|A| + |B|) / 2) × 100. The first has a sign and a reference value. The second has neither, so 12 and 15 give 22.2222% in either order. Two values with opposite signs always give 200%, so the figure says little there. If both values are 0, the calculator shows 0%.