Percent Error Calculator
Find the percentage error between an observed (measured) value and the true (accepted) value of a measurement. Modify the values and click "Calculate" to see the result with its steps.
Percentage Error
Percentage error measures the discrepancy between an observed (measured) value and a true (expected, accepted, or known) value. It is the standard way to compare a measurement against a known value and to judge whether the measurement can be trusted. Measured values almost always drift at least slightly from the true value — because of human error, estimations, or the limits of the instruments used — and percent error quantifies how large that drift is relative to the true value. A small percent error means the observed and true values are close; a large one means they differ greatly, and in most fields a small error is what you want. A very large error, such as 90%, usually means something went wrong, or that the experiment or measurement technique needs to be re-evaluated.
Computing percentage error
Start with the absolute error — the size of the gap between the two values. Divide it by the true value to get the relative error, then multiply by 100 to express it as a percentage. Keeping the sign of the difference (rather than its absolute value) also shows the direction of the error:
Absolute error = |Vobserved − Vtrue|
Relative error = |Vobserved − Vtrue|Vtrue
Percentage error = Vobserved − VtrueVtrue × 100%
For example, with an observed value of 56.891 and a true value of 62.327, the percentage error is 56.891 − 62.32762.327 × 100% = −8.7217% — the measurement is about 8.72% below the true value. These formulas assume the true value is known. When it is not, the spread of repeated measurements is usually summarized with a standard deviation instead.
Negative percentage error
If the absolute value of the difference is used, percent error is always positive (for a positive true value) and only the size of the error is reported. Dropping the absolute value, as this calculator does, lets the error be negative: an observed value of 7 against a true value of 9 gives 7 − 99 × 100% = −22.2222%. The negative sign simply means the measured value came in smaller than expected; if the observed value is larger, the error is positive. A negative error is neither better nor worse than a positive one of the same magnitude — the best possible outcome is 0%, when the observed and true values are equal.
Frequently Asked Questions
What is the formula for percent error?
Percent error = (observed value − true value) / true value × 100%. The sign shows the direction of the error: a positive result means the observed value is larger than the true value, and a negative result means it is smaller. Taking the absolute value gives the size of the error without its direction.
Can percent error be negative?
Yes. When the observed value is smaller than the true value, the signed percent error is negative — for example, an observed value of 7 against a true value of 9 gives (7 − 9) / 9 × 100% = −22.2222%. A negative error is not better or worse than a positive one of the same size; the best possible result is 0%, when the two values agree exactly.
What does a percent error of 0% mean?
It means the observed value equals the true value exactly, so there is no discrepancy between the measurement and the accepted value.
What happens if the true value is 0?
Percent error is not defined for a true value of 0, because the formula divides by the true value. If the observed value is non-zero the error is infinitely large relative to a true value of zero; if both values are 0, the error is 0%.