Uncertainty and error

Every measurement carries an uncertainty — a range within which the true value is expected to lie, honestly acknowledging the limits of the instrument and the person using it. Reporting "12.3 ± 0.1 cm" isn't a confession that a mistake was made; it's an accurate description of what the measurement can and can't tell you.

Error is a related but different idea: the actual difference between a measured value and the true value. The catch is that the true value is usually unknown — if you knew it exactly, you wouldn't need to measure it — so the error itself is rarely something you can calculate directly. The uncertainty is your best estimate of how large that unknown error probably is.

Errors split into two families that need different treatment. Random errors scatter results above and below the true value unpredictably, and averaging repeated measurements reduces their effect. Systematic errors push every result the same way, such as a scale with an unzeroed offset, and no amount of repetition fixes that — only finding and correcting the source does.