# 2.1.3 Calculating Uncertainty

### 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  ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
Close Close