Basic and Derived Units
Simple Explanation
A basic (or base) unit measures one of the handful of fundamental physical quantities that cannot be broken down into anything simpler — length, mass, time, electric current, temperature, amount of substance, and luminous intensity. A derived unit is built by combining base units through multiplication or division — for example, speed (metres per second) is length divided by time.
Why Do We Need It?
Every physical quantity in science, no matter how complicated, can be expressed using just these seven base units combined together — this is what lets physicists check whether an equation even makes sense, before checking whether the numbers are right.
Worked Example
Find the base units that make up the newton (the unit of force)
Force is defined by F = ma (mass × acceleration). Express the newton in terms of base units.
Why Does This Work?
Because every derived quantity is defined by a mathematical relationship (like F = ma), substituting the base units for each quantity in that relationship automatically gives the correct combination of base units for the derived unit — this is called dimensional consistency.
Real-Life Example
Checking an engineering formula by its units
An engineer derives a new formula and wants to sanity-check it before using it.
If the units on both sides of the formula do not reduce to the same combination of base units, the formula must be wrong — this quick check catches many algebra mistakes before they cause real problems.
Practice
Which of these is a base (basic) quantity, not a derived one?
EasyPressure is defined as force divided by area. In base units, what is the unit of pressure?
MediumCommon mistake
Treating a derived unit (like the newton or the pascal) as though it were fundamental — every named derived unit is really just a shorthand for a specific combination of the seven base units.
Quick Review
- Base units measure the seven fundamental quantities: length, mass, time, current, temperature, amount of substance, luminous intensity.
- Derived units are built by combining base units (e.g. speed = length/time).
- Checking that units match on both sides of an equation is a fast way to catch mistakes.