How this instrument works
Percent error measures how far a measurement landed from the value it was aiming at, expressed as a fraction of that target. The formula takes the absolute difference between measured and actual, divides by the size of the actual value, and scales by 100. The division is the crucial step: being off by 0.5 means little until you know whether the target was 10 or 10,000. Against 10 it is a 5% miss; against 10,000, a rounding whisper of 0.005%.
The absolute-value bars do two jobs. On top, |measured − actual| discards the direction of the miss, so overshooting by 0.5 scores the same as undershooting by 0.5. Underneath, |actual| keeps the denominator positive even when the reference itself is negative — a thermometer reading −4.9 °C against a true −5 °C is a clean 2% error, not a nonsense negative one.
One asymmetry is worth knowing: the formula treats the actual value as the reference, so swapping the two numbers changes the answer. 9.5 measured against 10 gives 5%; 10 against 9.5 gives 5.263%. When neither figure is authoritative, the symmetric cousin — percent difference, which divides by the average of the two — is the fairer instrument.
- Type your reading into the Measured value field — the number your instrument, experiment, or estimate produced.
- Enter the reference into the Actual value field: the accepted, true, or specification figure you are judging against.
- Read Percent error (%) — the absolute deviation as a share of the actual value, shown to three decimals.
- Signs are handled for you: negative readings are fine, and overshooting scores the same as undershooting.
Worked example — a 10-ohm resistor reads 9.5
A resistor stamped 10 Ω goes on the multimeter and reads 9.5 Ω. The miss: |9.5 − 10| = 0.5. Divide by the size of the target: 0.5 ⁄ 10 = 0.05. Scale to percent: 0.05 × 100 = 5. The component sits exactly 5% off its nominal value — precisely on the boundary of its gold-band ±5% tolerance, so it passes, barely.
Notice what the division bought. An absolute miss of half an ohm sounds small in isolation, but the percentage puts it in context: the same 0.5 Ω off a 100 Ω resistor would be 0.5%, comfortably inside even a brown-band 1% part. Percent error is the number that lets those two situations be compared at all.
Questions
Can percent error be negative?
Not with this formula — the absolute-value bars in |measured − actual| erase the sign, so 9.5 against 10 and 10.5 against 10 both give 5%. Some lab courses drop the bars deliberately so that a negative result flags an undershoot; if your instructor wants the signed version, compute (measured − actual) ⁄ actual × 100 and keep the sign.
What happens when the actual value is zero?
The formula breaks: dividing by |0| is undefined, so this instrument refuses the input rather than reporting infinity. A relative comparison against a zero reference is meaningless — every nonzero miss is infinitely large in proportional terms. Judge such measurements with absolute error, measured − actual, in the original units instead.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known true value; percent difference compares two measurements when neither is authoritative, dividing by their average rather than by one of them. 9.5 vs 10 gives a 5% error but a 5.128% difference (0.5 ⁄ 9.75). Use error when a textbook, standard, or specification defines the target; use difference when checking two instruments against each other.
Is a 5% error good or bad?
It depends entirely on the field. Introductory chemistry labs often accept 5% as respectable; a machinist holding a ±0.1% tolerance would reject it instantly; population estimates routinely tolerate far more. The number carries no verdict on its own — compare it against the tolerance your context specifies, like the ±5% gold band on a resistor or the stated uncertainty of a reference standard.
How is percent error different from percent change?
Percent change tracks one quantity moving over time — (new − old) ⁄ old × 100, sign kept, because direction matters for growth and decline. Percent error judges a reading against a fixed truth and usually discards the sign. Same arithmetic skeleton, different question: change asks how much something moved; error asks how far off you were.