What Is Percentage Error and How Is It Calculated?
Learn what percentage error means, how to calculate it, and how absolute error, relative error, and percentage error differ.
A student measures the boiling point of water at sea level as 99°C in a lab. The accepted value is 100°C. Was the experiment accurate? Percentage error turns that question into a single, comparable number — in this case, 1% — that works regardless of what's being measured or what units it's in.
Measured value vs. true value
Percentage error measures how far an observed or measured value strays from a known, accepted, or true value, expressed as a percentage of that true value. It's specifically an accuracy measure — it assumes there's a correct answer to compare against, which sets it apart from calculations that just compare two arbitrary values.
The formula
Percentage Error = (|Observed Value − Accepted Value| ÷ Accepted Value) × 100
The accepted (true) value is always the denominator, because that's the fixed reference point the observed value is being measured against — the same role the "original value" plays in a standard percentage change calculation.
A worked example
Measured boiling point: 99°C. Accepted value: 100°C.
Percentage Error = |99 − 100| ÷ 100 × 100 = 1 ÷ 100 × 100 = 1%
A second example: a scale reads a 5kg weight as 5.3kg.
Percentage Error = |5.3 − 5| ÷ 5 × 100 = 0.3 ÷ 5 × 100 = 6%
Absolute error vs. percentage error
Absolute error is simply the raw difference between the observed and accepted values, in the original units — 1°C in the boiling-point example, 0.3kg in the scale example. Percentage error takes that same raw difference and expresses it as a share of the accepted value, which makes it possible to compare accuracy across completely different measurements. A 1°C error out of 100°C (1%) and a 0.3kg error out of 5kg (6%) aren't directly comparable as raw numbers, but their percentage errors show the scale measurement was proportionally far less accurate.
Percentage error vs. percentage difference
These two are easy to confuse because they look structurally similar, but they answer different questions — and use different denominators. Percentage error assumes one value (the accepted value) is the known truth, and divides by that value. Percentage difference, covered in our article, is for comparing two values neither of which is a known truth, and divides by their average instead.
Using percentage difference's average-based formula on an accuracy question would give a different, incorrect number, since it doesn't treat the accepted value as special. If you're checking how accurate a measurement is against a known standard, percentage error's original-value-style formula is what applies — in practice, that's the same calculation used by our and (using the accepted value as the "original" and the observed value as the "new" value, then taking the absolute value of the result).
Signed vs. absolute error
The formula above uses an absolute value, which only reports the size of the error, not its direction. In scientific and engineering contexts, it's sometimes useful to keep the sign: (Observed − Accepted) ÷ Accepted × 100, without the absolute value bars. A positive signed error means the measurement overshot the true value; negative means it undershot. This distinction matters when checking for a consistent bias in an instrument or method — a scale that's always a bit high tells a different story than one that's randomly high or low.
Where this is used
Percentage error is standard in lab sciences (comparing an experimental result to a known constant), manufacturing and calibration (checking how far an instrument's reading is from a certified reference), and forecasting (comparing a predicted value to what actually happened). The U.S. National Institute of Standards and Technology (NIST) discusses the related concept of measurement error and uncertainty in metrology in more depth in its public guidance.
Limitations
Percentage error is only meaningful when there's a genuine accepted or true value to compare against, and that value isn't zero (division by zero is undefined, the same limitation that applies to percentage change). It also says nothing about why a measurement was off — a small percentage error doesn't rule out a systematic bias, and a large one doesn't necessarily mean the method is flawed rather than the equipment being uncalibrated. It's a starting diagnostic, not a full explanation.
Sources:
Frequently Asked Questions
Try it yourself
Use the Percentage Calculator to run this calculation with your own numbers.