IB Physics HLTool 3 — MathematicsPractical SkillsSI units & prefixes~13 min read
Base & Derived Units
Every measurement in physics is built from a tiny set of base units — just seven of them. The newton, the joule, the volt and everything else are derived by combining these. Understanding how units are built (and how prefixes scale them) lets you check equations, catch mistakes, and convert between quantities with confidence.
📚 What you need to know
There are 7 SI base units; IB Physics uses 6 of them (not the candela)
All other units are derived by combining base units
Derive a unit from the definition of the quantity (e.g. force = mass × acceleration)
Prefixes (k, m, µ, M…) scale a unit by a power of 10
Checking units on both sides of an equation is dimensional analysis
Some non-SI units (eV, light year, kW h) are common and convertible
The seven base units
Everything in the SI system starts here. These base units are defined independently, and each one measures a single fundamental quantity.
Quantity
Unit name
Symbol
length
metre
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
temperature
kelvin
K
amount of substance
mole
mol
luminous intensity
candela
cd
You only really need six of these for IB Physics — the candela (luminous intensity) doesn’t appear in the course. The other six, though, are worth knowing cold, because every derived unit you’ll ever meet is just these building blocks stuck together.
Deriving units
A derived unit is built by combining base units, following the definition of the quantity. You don’t memorise them — you work them out. The trick is to take the defining equation and substitute the base units in.
Take the definition, substitute the base units, and the derived unit falls out: force = mass × acceleration gives the newton = kg m s⁻².
Here are the most common derived units and what they break down to. Notice how each one is just base units in disguise.
Derived unit
Quantity
In base units
newton (N)
force
kg m s−2
joule (J)
energy
kg m2 s−2
pascal (Pa)
pressure
kg m−1 s−2
watt (W)
power
kg m2 s−3
coulomb (C)
charge
A s
volt (V)
potential difference
kg m2 s−3 A−1
WE 1
Energy is force × distance. Use this to express the joule in SI base units.
Step 1 — start from the newton
force has units kg m s−2 (the newton)
Step 2 — multiply by distance (metres)
J = N × m = kg m s−2 × m = kg m2 s−2joule = kg m² s−2You just build derived units up one definition at a time — energy is force through a distance, so you tack an extra metre onto the newton.
Prefixes
Physics deals with the tiny (the size of an atom) and the huge (the distance to a star). Rather than write endless zeros, we attach a prefix that multiplies the unit by a power of 10.
Prefixes scale a unit by powers of 10 — smaller than the base on the left (red), larger on the right (teal).
Prefix
Symbol
Value
giga
G
109
mega
M
106
kilo
k
103
centi
c
10−2
milli
m
10−3
micro
µ
10−6
nano
n
10−9
WE 2
A household uses 2500 kW h of electricity. Given 1 kW h = 3.60 × 106 J, express this energy in joules.
Step 1 — recall the conversion
1 kW h = 3.60 × 106 JStep 2 — multiply
2500 × (3.60 × 106) = 9.00 × 109 J9.00 × 10⁹ JThe kilowatt-hour is a non-SI energy unit (energy = power × time). Converting it to joules is just a matter of applying the given relationship.
Checking equations with units
One of the most useful things base units let you do is check an equation. If both sides don’t reduce to the same combination of base units, the equation is wrong — this is called dimensional analysis (or checking “homogeneity”).
This is a genuine exam superpower. Before you trust a rearranged equation, put the units through it. If the left side comes out as kg m s−2 and the right side doesn’t, you’ve made a slip — and you’ve caught it before losing any marks on the numbers. It costs ten seconds and saves whole questions.
💡 Top tips
There are 7 base units; IB uses 6 (skip the candela).
Derive units from the quantity’s definition — don’t memorise them.
Prefixes are just powers of 10: k = 10³, m = 10−3, µ = 10−6.
Use dimensional analysis to sanity-check any equation.
Convert non-SI units (eV, kW h) using the given relationships.
⚠ Common mistakes
Mixing up prefixes — e.g. treating milli (10−3) as micro (10−6)
Forgetting to convert prefixes to base units before calculating
Getting the sign of a power wrong (10−2 vs 102)
Assuming a derived unit can’t be broken down into base units
Skipping the unit check that would have caught an algebra error
Quick recap: All units come from 7 SI base units (IB uses 6). Derived units like the newton (kg m s−2) and joule (kg m² s−2) are built from the quantity’s definition. Prefixes scale by powers of 10. Checking that units match on both sides of an equation is dimensional analysis.
You’ve now seen that units can be broken down and rebuilt. The natural next move is to use that idea as a tool: taking an unfamiliar equation and checking — or even working out — the units of a mystery quantity. That’s exactly what Dimensional Analysis is all about, and it’s next.
Units and prefixes tripping you up?
Book a free meeting and we’ll drill deriving units, converting prefixes cleanly, and using unit-checks to catch mistakes — the quiet skills that stop silly errors across every topic.
