Understanding Percentage Error
Percentage error is a measurement of the discrepancy between an observed (measured) value and a true (expected, accepted, known) value. It is widely used in science, manufacturing, and engineering to evaluate the accuracy of a measurement or an estimation.
Why Do We Need It?
When measuring data, such as the boiling point of a liquid or the weight of an object, the measured value often varies slightly from the true value. This error can arise from human error, estimation, or device limitations. Calculating the percent error gives a context to the magnitude of the mistake. An error of 1 cm might be terrible if you're measuring a microscopic object, but completely negligible if you're measuring a football field. Percent error normalizes this discrepancy.
Formulas
- Absolute Error|Observed - True|
- Relative ErrorAbsolute Error / |True|
- Percentage ErrorRelative Error × 100%
Negative vs. Positive Percentage Error
By standard definition, percentage error is calculated using the absolute value of the difference, meaning it is always a positive number. In most scientific contexts, we only care about the magnitude of the error, not the direction.
However, sometimes researchers preserve the sign to indicate the direction of the error. A negative percentage error means the observed value is smaller than the true value, while a positive percentage error means the observed value is larger. Our calculator computes both the strict magnitude (Percentage Error) and the Directional Error.