Base Quantities and Units
A physical quantity consists of a numerical magnitude and a unit. Together, these elements form the foundation of standardized measurement, enabling scientists and researchers to describe and understand the physical world with accuracy and clarity.
There are several fundamental base quantities, each with its associated unit of measurement.
| Base quantity | Base unit | Description |
| Mass | kilograms (kg) | a fundamental property of matter and represents the amount of substance within an object |
| Length | metres (m) | quantifies the spatial extent or size of an object or distance between two points |
| Time | seconds (s) | foundational dimension for measuring the progression of events or the duration of processes |
| Current | Amperes (A) | represents the rate of flow of electric charge |
| Temperature | Kelvins (K) | a measure of the average internal kinetic energy of particles in a system, with absolute zero as its starting point |
| Amount of Substance | Mole (mol) | quantifies the number of entities (atoms, molecules) in a given sample |
These base quantities and their respective units form the basis for all other derived quantities used in scientific measurements and calculations.
Derived Quantities and Units
Derived quantities in the realm of science and measurement are quantities that are derived from one or more base quantities by mathematical or logical operations. These operations can include addition, subtraction, multiplication, division, and exponentiation.
Examples of derived quantities include:
- velocity (which is derived from length and time)
- acceleration (derived from changes in velocity over time)
- area (derived from multiplying length by length)
- power (derived from energy divided by time)
Prefixes
Prefixes make it simpler to work with measurements that can vary widely in size. They allow us to express quantities in a more manageable way and understand the scale of what you’re measuring.
| Prefix | Abbreviation | Relationship to Basic Unit | Exponential Relationship to Basic Unit |
| tera | T | 1,000,000,000,000 x unit | 1012 x unit |
| giga | G | 1,000,000,000 x unit | 109 x unit |
| mega | M | 1,000,000 x unit | 106 x unit |
| kilo | k | 1,000 x unit | 103 x unit |
| deci | d | 1/10 x unit | 10-1 x unit |
| centi | c | 1/100 x unit | 10-2 x unit |
| milli | m | 1/1000 x unit | 10-3 x unit |
| micro | μ | 1/1,000,000 x unit | 10-6 x unit |
| nano | n | 1/1,000,000,000 x unit | 10-9 x unit |
Conversion of Units
When converting a physical quantity involving derived units, such as for speed, one can work the different units out separately. For example,
$60 \text{ km h}^{-1} = \dfrac{60 \text{ km}}{1 \text{ h}} = \dfrac{60 000 \text{ m}}{60 \times 60 \text{ s}} = 16.7 \text{ m s}^{-1}$
It’s common to encounter various units for the same physical quantity, such as metres (m) and kilometres (km) for length, or grams per cubic centimetre (g cm-3) and kilograms per cubic metre (kg m-3). To facilitate accurate analysis and comparison, unit conversions are applied using conversion factors based on established relationships between different units.
The following applet allows you to practise conversion of some common units.