Calculating Uncertainties (AQA A Level Physics): Revision Note

Uncertainty

• There is always a degree of uncertainty when measurements are taken

• The uncertainty can be thought of as the difference between the actual reading taken (caused by the equipment or techniques used) and the true value

• Uncertainties are not the same as errors

  • Errors can be thought of as issues with equipment or methodology that cause a reading to be different from the true value

  • The uncertainty is a range of values around a measurement within which the true value is expected to lie, and is an estimate

• For example, if the true value of the mass of a box is 950 g, but a systematic error with a balance gives an actual reading of 952 g, the uncertainty is ±2 g

• These uncertainties can be represented in a number of ways:

  • Absolute uncertainty: where uncertainty is given as a fixed quantity

  • Fractional uncertainty: where uncertainty is given as a fraction of the measurement

  • Percentage uncertainty: where uncertainty is given as a percentage of the measurement

$\mathrm{percentage}\mathrm{uncertainty}=\frac{\mathrm{uncertainty}}{\mathrm{measured}\mathrm{value}}\times 100\%$

• To find uncertainties in different situations:

  • The uncertainty in a reading: ± half the smallest division

  • The uncertainty in a measurement: at least ±1 smallest division

  • The uncertainty in repeated data: half the range i.e. ± ½ (largest - smallest value)

  • The uncertainty in digital readings: ± the last significant digit unless otherwise quoted

Combining uncertainties

• When combining uncertainties, the rules are as follows:

Adding / subtracting data

• Add together the absolute uncertainties

Multiplying / dividing data

• Add the percentage or fractional uncertainties

Raising to a power

• Multiply the percentage uncertainty by the power