Base quantities and SI units
Key idea: Derived quantities combine base quantities, and their units follow the same relationships. A named SI unit such as the newton can still be a derived unit.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Recall the six quantity-unit pairs, then check the table.
- Follow how derived quantities combine base quantities.
- Identify the base quantities and explain how the others combine base quantities.
- Compare each relationship with its unit and read the newton’s base-unit form.
- Explain why force and the newton are derived.
- Choose units that give the requested final unit.
- Convert distance and elapsed time before calculating the requested speed.
- Calculate density in the units the question requests.
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ContinueA physical quantity is a property you can measure, written as a number and a unit. In a length of 2.5 m, 2.5 is the number and m is the unit. The same length can be written as 250 cm: changing the unit changes the number, not the length.
The six base quantities
Every quantity in physics can be built from a small starting set, the base quantities. Recall these six and their SI units:
| Base quantity | Quantity symbol | SI unit | Unit symbol |
|---|---|---|---|
| mass | m | kilogram | kg |
| length | l | metre | m |
| time | t | second | s |
| electric current | I | ampere | A |
| temperature | T | kelvin | K |
| amount of substance | n | mole | mol |
The full SI has a seventh base quantity, luminous intensity, measured in candela (cd). You need to recall only the six in the table.
A quantity symbol and a unit symbol do different jobs. In a formula, italic m stands for mass; after a number, upright m means metre. Read the context to tell them apart.
Worked example 1
Identify base quantities
Problem
From mass, speed, time, force and electric current, identify the base quantities.
Show full solution
Test how each quantity is defined
Method
Look for quantities that are defined from other quantities.
Reason
A derived quantity is built from base quantities by a relationship.
Working
Answer
Speed is length divided by time; force is mass multiplied by acceleration.
Classify the list
Method
Mass, time and electric current are base quantities.
Reason
They are in the base-quantity list.Working
Answer
Base: mass, time, electric current. Derived: speed, force.
Quick check
Check your understanding 1
From length, area, time and energy, identify the base quantities and explain why the other two are derived.
Show answer
Length and time are base quantities. Area is length multiplied by length. Energy is force multiplied by distance, and force is mass multiplied by acceleration. Area and energy are both built from base quantities, so they are derived.
Derived quantities and their units
A derived quantity is defined from base quantities, and its unit comes from the same relationship.
| Derived quantity | Relationship | Unit |
|---|---|---|
| speed | distance ÷ time | m s⁻¹ |
| acceleration | change in velocity ÷ time | m s⁻² |
| density | mass ÷ volume | kg m⁻³ or g cm⁻³ |
| force | mass × acceleration | N |
Some derived units have their own names: the newton (N), joule (J) and pascal (Pa). They are SI units, but not SI base units. The newton is shorthand for kg m s⁻².
Spot the mistake 2
A newton is not a base unit
Learner response
A student says: “Force must be a base quantity because the newton is an SI unit.” Find the error and express the newton in base units.
Use the defining relationship
Show solution step by step
Identify the defining relationship
Method
Use F = ma: force is mass multiplied by acceleration.Reason
Force is defined from mass and acceleration, so it is derived.Working
Answer
Unit of force = unit of mass × unit of accelerationSubstitute base units
Method
Replace mass by kilograms and acceleration by metres per second squared.Reason
A named SI unit can still be a derived unit.Working
Answer
1 N = 1 kg m s⁻²
Common mistake
Keep units consistent in a calculation
An equation gives the right answer only if the units you put in are consistent with each other. Convert the inputs so that they produce the unit the question asks for.
You do not always have to convert to SI base units. Density can be calculated directly in g cm⁻³ when mass is in grams and volume is in cubic centimetres. Convert only if the answer is wanted in kg m⁻³.
Guided practice 3
Convert for the requested unit
Problem
Match both inputs to the requested unit
Show the steps Optional working
Hints
Hint 1
read the requested unit
The answer must be in metres divided by seconds.
Hint 2
convert both inputs
Convert the distance to 1200 m and the elapsed time to 150 s.
Show solution step by step
Convert distance and time
Method
Express the inputs in metres and seconds.Reason
Metres divided by seconds gives the requested m s⁻¹.Working
Answer
1.2 km = 1200 m, 2.5 min = 150 sCalculate average speed
Method
Divide distance by time.Reason
Average speed is total distance divided by total time.Working
Answer
v = (1200 m)/(150 s) = 8.0 m s⁻¹
Quick check
Check your understanding 2
A sample has mass 54.0 g and volume 20.0 cm³. Calculate its density in g/cm³. Must you convert the inputs first?
Show answer
Grams divided by cubic centimetres already gives the requested unit. You would convert to kilograms and cubic metres only if the answer were wanted in kg m⁻³.
Before writing a final answer, check that the input units are consistent, that the calculation gives the kind of unit asked for, and that the unit is written after the number. In a results table, put the unit in the column heading, for example “length / cm”.
Common mistakes
- Calling a familiar derived quantity, such as speed, a base quantity.
- Giving the quantity name when the question asks for its SI unit, or giving only a unit symbol when the quantity is asked for.
- Mixing units in one calculation, such as kilometres with seconds.
Spotted an error? Report a correction
Syllabus and review details
- SEC G3 Physics 2027 · 2027
Content Structure, PDF page 9; Subject Content, PDF pages 10–28