Uncertainty and errors

No measurement is perfect. Uncertainty says how far the true value might be from your reading. Random errors scatter results; systematic errors shift them all the same way.

Key facts

  • Repeat readings and take a mean to reduce random error.
  • Uncertainty ≈ half the range of repeated readings.
  • Percentage uncertainty = uncertainty ÷ value × 100.
  • Zero errors and badly calibrated instruments cause systematic errors.
  • Adding or subtracting: add absolute uncertainties. Multiplying or dividing: add percentage uncertainties.

Worked examples

Example 1

Times measured: 2.31 s, 2.28 s, 2.35 s, 2.30 s. Give the mean with its uncertainty.

  1. Mean: (2.31 + 2.28 + 2.35 + 2.30) ÷ 4 = 2.31
  2. Range: 2.35 − 2.28 = 0.07, half is about 0.04.
  3. 2.31 ± 0.04 s

Answer: 2.31 ± 0.04 s