Calculating 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
- 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
How to calculate absolute, fractional and percentage uncertainty
Combining Uncertainties
- The rules to follow
- Adding / subtracting data – add the absolute uncertainties
- Multiplying / dividing data – add the percentage uncertainties
- Raising to a power – multiply the fractional (or %) uncertainty by the power
