# 1.2.2 Calculating Uncertainties

### 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

• Always make sure your absolute or percentage uncertainty is to the same number of significant figures as the reading

### Combining Uncertainties

• When combining uncertainties, the rules are as follows:

• Add together the absolute uncertainties #### Exam Tip

Remember:

• Absolute uncertainties (denoted by Δ) have the same units as the quantity
• Percentage uncertainties have no units
• The uncertainty in numbers and constants, such as π, is taken to be zero

Uncertainties in trigonometric and logarithmic functions will not be tested in the exam, so just remember these rules and you’ll be fine! ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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