error

Error is the difference between a value and its true or intended value. In everyday language it denotes a mistake or fault, but in technical usage it denotes a deviation that arises from limitations in measurement, observation, calculation, or interpretation.

In measurement and experiments: A measurement error is the difference between the observed value and the true value. Errors are typically classified as systematic (bias that shifts results in one direction) or random (unpredictable fluctuations). The terms accuracy (closeness to the true value) and precision (repeatability) are used to describe quality. Uncertainty quantifies the doubt about a measurement, and results are often presented with an estimated confidence interval or standard deviation.

In statistics and data analysis, the observed difference between a statistic and a population parameter is called an error or residual. Sampling error arises from observing a sample rather than the entire population. In computing, an error can be an incorrect result produced by a program, or an invalid state detected during execution. Computers use error handling, including error codes and exceptions, to report and recover from errors. Error propagation describes how input uncertainties spread through calculations to affect outputs.

Beyond measurements and computing, error appears in philosophy as false belief or reasoning; in information theory, error-detecting and error-correcting codes mitigate data corruption. In practice, systems aim to minimize error through calibration, redundancy, validation, and robust design.