Math Playground
Measurement

Error in measurement

Every measurement has uncertainty — quantify it, report it, propagate it.

Every measurement has uncertainty. Sources: instrument resolution, observer reading, and random fluctuation.

Try this
196
absolute, relative & percent error = Absolute error = 4 | Relative = 0.0200 | Percent = 2.00%
Percent error

Absolute error is the top of the fraction; relative error is the fraction before the ×100%.

Where uncertainty comes from

No measurement is perfect. Errors creep in from the instrument's resolution (a ruler marked in mm can't see tenths of a mm), the person reading it (parallax, judgement), and random fluctuation (temperature, vibration). Good practice: report a value *with* its uncertainty, like 4.2 ± 0.1 cm.

Your turn

True length 50 cm; you measure 48 cm. What's the percent error?

Error types

  • Absolute error — the size of the discrepancy.
  • Relative error — error divided by true value.
  • Percent error — relative error × 100%.