Errors, Uncertainty, Precision, and Accuracy

No measurement is ever perfect. Every experimental value carries an uncertainty that describes the range within which the true value is likely to lie. Understanding the sources of error and reporting uncertainty honestly is central to experimental physics.

Random versus systematic errors

Errors fall into two broad categories.

Random errors cause measurements to scatter unpredictably above and below the true value. They arise from uncontrollable fluctuations: slight variations in reading a scale, electrical noise, small changes in conditions, or the limits of human reaction time. Because random errors are equally likely to be positive or negative, taking repeated measurements and averaging reduces their effect — the more readings you take, the more the scatter tends to cancel out.

Systemati