What percent error measures
Percent error tells you how far a measured or experimental value is from the accepted or theoretical value, as a share of the accepted value. In a lab report it answers the question of how accurate your result was: a 2% error means your measurement missed the reference by 2% of its size. Because it is relative, you can compare the accuracy of a measurement of a few grams with one of several kilometers.
Worked example
A pendulum experiment gives 9.72 m/s² for the acceleration of gravity. Compare it with the standard acceleration of gravity, which the NIST list of CODATA values gives as exactly 9.80665 m/s².
- Subtract the accepted value from the measured value: 9.72 − 9.80665 = −0.08665.
- Take the absolute value: |−0.08665| = 0.08665. This is the absolute error, in m/s².
- Divide by the accepted value: 0.08665 ÷ 9.80665 ≈ 0.0088358. This is the relative error.
- Multiply by 100: the percent error is about 0.88%.
With the signed formula the result is about −0.88%, which also says that the measurement came out low.
Absolute or signed percent error
With absolute value bars around the difference, percent error is always zero or positive and only says how far off you were. Without the bars you get the signed percent error, which keeps the direction: a negative percent error means the measured value is below the accepted one, a positive one means above. Both versions divide by the size of the accepted value, so the sign of the result always matches the direction of the miss, even when the accepted value itself is negative, like a temperature below zero. If your instructions do not say which version to use, use the absolute one and mention the direction in words.
Percent difference is a different formula
Percent error needs a reference: one value is right by definition or by agreement, and the other is checked against it. When you compare two measurements of equal standing, like the results of two lab groups or two methods, neither is the reference. Percent difference then divides the gap by the average of the two values, so swapping A and B gives the same result.
The two formulas give different numbers for the same pair. For 48 and 50, percent error with 50 as the accepted value is 4%, but the percent difference is |48 − 50| ÷ 49 × 100 ≈ 4.08%. Do not mix them up in a lab report. Percent difference only makes sense for two values with the same sign, since an average near zero would blow the result up; the calculator tells you when that happens. To see how much a value grew or shrank from a starting point, use the percentage change calculator instead, which divides by the starting value.
When the accepted value is zero
Percent error divides by the accepted value, so it does not exist when that value is 0. A temperature measured at 0.3 °C against an expected 0 °C would be an infinite percent off, which tells you nothing. In that case report the absolute error, 0.3 °C, or compare in a unit where the reference is not zero, such as kelvins. The calculator shows the absolute error and explains this instead of printing a meaningless number.
Exact arithmetic and rounding
The calculator keeps your values as exact decimals and rounds only once, at the end, to the decimal places you choose. That avoids rounding twice, which can change the last digit, and avoids the tiny errors of binary floating point arithmetic, where 0.3 − 0.1 comes out as 0.19999999999999998. If the exact percent ends within the chosen places, it is shown in full; otherwise it is rounded half away from zero. The steps show the unrounded value too. How many digits to report is a question of significant figures: the percent error should not look more precise than your measurement.
Common mistakes
- Dividing by the measured value. Percent error always divides by the accepted value. 48 against 50 is 4%, but dividing by 48 would give about 4.17%.
- Forgetting to multiply by 100. 0.04 is the relative error; the percent error is 4%.
- Mixing units. A measurement in centimeters against an accepted value in meters gives a meaningless result. Convert first, then compare.
- Rounding too early. Keep all digits of the difference and round only the final percent.
How to use the percent error calculator
- 1Choose percent error to compare a measurement with an accepted value, or percent difference to compare two measurements of equal standing.
- 2Type the measured (experimental) value and the accepted (theoretical) value in the same unit.
- 3Pick absolute or signed percent error and the number of decimal places to round to.
- 4Read the result and the steps of the formula, then copy the result or a link that opens the calculator with your values.
Sources
- Standard acceleration of gravity, NIST reference on constants, units and uncertainty (2022 CODATA values): 9.80665 m/s², exact
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100. Subtract the accepted value from your measured value, drop the sign, divide by the accepted value and multiply by 100. A measured 48 against an accepted 50 gives |48 − 50| ÷ 50 × 100 = 4%.
Can percent error be negative?
The usual percent error uses the absolute value, so it is never negative. A signed version keeps the sign instead: (measured − accepted) ÷ |accepted| × 100. Then a negative result means your measurement came out below the accepted value and a positive one means above it. Switch to "Signed" to see that version.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known accepted value, so it divides by the accepted value. Percent difference compares two values where neither is the reference, like two students' measurements, so it divides by their average: |A − B| ÷ ((A + B) ÷ 2) × 100. For 48 and 50, percent error is 4%, while the percent difference is about 4.08%.
What if the accepted value is zero?
Then percent error is undefined, because you would divide by zero. Any measurement, however close, would be infinitely far off in percent. Report the absolute error, |measured − accepted|, in the units of your measurement instead. The calculator shows it in that case.
What is a good percent error?
There is no universal cutoff. It depends on the instruments, the method and what your teacher or field expects. A percent error is most useful next to the uncertainty of your measurement: if the accepted value lies within your measurement's uncertainty, the difference can be explained by that uncertainty alone.
Is percent error the same as relative error?
Nearly. The relative error is |measured − accepted| ÷ |accepted| as a plain number, like 0.04. Percent error is the same number times 100, so 0.04 becomes 4%. The calculator shows both.