Percent error is one of 1 measurement formula in the arithmetic section of this library, and it is used at middle school · high school level.
Why percent error works
The gap between what you measured and what was expected only matters relative to the size of the thing being measured. Missing by 0.2 is serious on a value of 1 and trivial on a value of 1000. Dividing by the accepted value scales the miss, and the absolute value bars keep the focus on how far off you were rather than in which direction.
What each symbol means
measured is the experimental value and accepted is the reference value.
Percent error: when it holds
The accepted value must be nonzero and both values must use the same units.
When it stops applying
It cannot be used when the accepted value is 0, such as an experiment whose true answer is zero net charge, because you would be dividing by zero. Those results are reported as an absolute error with units instead.
Percent error: a worked example
Measured $9.8$ versus accepted $10$ gives $|9.8-10|/10=2\%$.
The mistake to avoid
What people do: Students divide by their own measured value instead of the accepted one.
Why it goes wrong: That makes the answer depend on how wrong you already were, so two people with different errors would be scored against different yardsticks.
Do this instead: Put the accepted value underneath every time. Measuring 9.8 against an accepted 10 gives 0.2/10 = 2 percent; dividing by 9.8 instead gives 2.04 percent, which is close here but drifts badly for larger errors.
Percent error: step by step
- Name the unknown, and the unit the answer has to come out in.
- Match the symbols to your values. measured is the experimental value and accepted is the reference value.
- Check the conditions before substituting. The accepted value must be nonzero and both values must use the same units.
- Substitute, keep exact values to the last line, then test the sign, size, and unit against a rough estimate — the check that catches most arithmetic slips.
Where this formula fits
- Subject
- Arithmetic formulas — 13 entries in this library
- Topic
- Measurement
- Level
- Middle school · High school
Formulas are easiest to keep when they sit inside a method rather than on a list. Use the links below to see where percent error comes from, to check a calculation against a tool, and to practise it until you can recall it without looking.
- Understanding Percentages — the lesson behind this formula: translate among percentages, decimals, and proportions.
- Arithmetic Calculator — check your substitution and the value it produces.
- Study arithmetic — the subject guide that explains the ideas these formulas compress.
- Arithmetic Practice — questions that make you retrieve the formula instead of recognising it.
- All 13 arithmetic formulas — the full grouped reference, or the complete formula library.
Questions about percent error
Is percent error the same as percent change?
No. Percent change compares a before and an after and keeps its sign, while percent error compares a measurement with a known truth and throws the sign away.
Can percent error be negative?
Not with the absolute value bars in place, since size is the point. Some lab courses drop the bars on purpose so the sign shows whether the measurement came in high or low.
What counts as a good percent error?
It depends on the equipment and the field entirely. A school lab might accept 5 percent, while a machine shop working to a thousandth of an inch would treat that as a ruined part.
Does a small percent error mean my work was careful?
Not by itself. Errors can cancel out by luck, and a value can be reproducible yet consistently biased. Precision and accuracy are separate things, and this formula measures only accuracy.