What this calculator does
Percent error expresses the gap between what you measured and what the value actually is, as a proportion of the true value. Scaling by the true value is what makes it comparable across different magnitudes.
The sign carries information the absolute version discards. A measurement of 9.8 against a true 10 gives a 2.00 per cent error, and the signed version of −2.00 per cent tells you it was an underestimate.
The formula
The difference between measured and accepted values is divided by the accepted value and multiplied by 100. The absolute version discards the sign; the signed version keeps it.
| Term | Meaning |
|---|---|
| Percent error | The absolute difference as a percentage of the accepted value. |
| Signed error | The same figure keeping its sign, showing direction. |
| Accepted value | The true or reference value, which forms the denominator. |
The inputs explained
| Field | What to enter |
|---|---|
| Measured value | The value you measured or calculated. |
| Accepted (true) value | The accepted or true value. Cannot be zero, since it is the denominator. |
When to use it
Reporting a laboratory result
Percent error is the standard way to state experimental accuracy.
Checking a calculation
Comparing an estimate against an exact answer quantifies how close it came.
Comparing across scales
A 1 unit error means something different at 10 than at 10,000.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the measurement change the error?
Three measurements against the same true value.
Questions
Why divide by the accepted value rather than the measured one?
Because the accepted value is the reference the error is being judged against. Dividing by the measurement would make the denominator itself uncertain, which defeats the purpose.
When should I use the signed version?
Whenever direction matters, which is often. A systematic bias shows up as errors consistently sharing a sign, and that pattern is invisible once absolute values are taken.
What if the accepted value is zero?
Percent error is undefined, since it would require dividing by zero. In that case absolute error is the only meaningful measure, and the calculator reports the problem rather than a result.
How does this differ from percent difference?
Percent difference compares two measurements with no agreed true value, dividing by their average instead. Percent error assumes one of the values is correct.
For rounding decimals to fractions, see the round to nearest fraction calculator. For relative error in statistics, see the relative error calculator.