2.1.1FoundationsFoundation

SI Units, Prefixes and Homogeneity

Every quantity you calculate in this course is a number attached to a unit — get the unit wrong and the number means nothing at all. Module 2 starts here for a reason: before you can trust any equation later in the course, you need to know exactly what it’s built from, and how to spot when a "derived" quantity has gone dimensionally wrong.

30 min Video by Physics Online Module 2.1 Physical quantities and units

Unit Prefixes — A Level PhysicsWatch the full walkthrough before the notes below.

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What you'll be able to do

State the six SI base quantities and units used throughout this course
Derive a derived unit from the defining equation of a quantity
Use homogeneity of units to test whether an equation could be correct
Convert between a value written with an SI prefix and standard form
Recognise the standard SI prefixes from pico to tera

Base quantities and units

Physics builds every measurement from a small set of independently-defined $base quantities$ : mass (kilogram, kg), length (metre, m), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), and amount of substance (mole, mol). Every other unit used across this specification — from newtons to farads — is a combination of these six.

A unit built from a combination of base units is a $derived unit$ . Some derived units are given their own special name (the newton, the joule, the ohm) purely for convenience, but they always reduce back to a combination of the six base units if you trace their defining equation.

Tip — If a question asks for an answer "in base units" or "in SI units", it wants kg, m, s (and A, K, mol where relevant) — never a named derived unit like N or J.

Deriving units and homogeneity

To find the units of any derived quantity, substitute the base units into its defining equation. Force, from $F = ma$ , has units $kg \times m s^{- 2} = kg m s^{- 2}$ — given the special name newton (N). Because every physically valid equation must balance dimensionally, checking that both sides reduce to the $same$ combination of base units — checking $homogeneity$ — is a genuinely useful way to test a derived or half-remembered formula.

Homogeneity can never prove an equation correct (a missing factor of 2 or $π$ makes no difference to the units), but it will immediately expose an equation that cannot possibly be right.

F = ma \Rightarrow N = kg m s^{- 2}

A derived unit, found from its defining equation.

1Left side: energy, units

kg m^{2} s^{- 2}

(the joule).

2Right side:

[m] [v]^{2} = kg \times (m s^{- 1})^{2} = kg m^{2} s^{- 2}

3Both sides match — the equation is homogeneous (the constant

\frac{1}{2}

carries no units, so it plays no part in this check).

AnswerBoth sides give kg m² s⁻² — the equation is dimensionally consistent.

Tip — Homogeneity checks are a fast way to catch an equation you’ve mis-remembered under exam pressure — if the units don’t match, you know immediately something is wrong, even before checking the physics.

Prefixes

SI prefixes attach a power-of-ten multiplier to a unit, letting you write extremely large or small quantities compactly. A value written with a prefix must always be converted to the plain SI unit (or standard form) before it is used in a calculation — mixing prefixed and unprefixed values in the same equation is one of the most common sources of an answer being wrong by a neat power of ten.

p = 1 0^{- 12}, n = 1 0^{- 9}, μ = 1 0^{- 6}, m = 1 0^{- 3}, c = 1 0^{- 2}, k = 1 0^{3}, M = 1 0^{6}, G = 1 0^{9}, T = 1 0^{12}

Common SI prefixes: pico, nano, micro, milli, centi, kilo, mega, giga, tera.

1nano means

\times 1 0^{- 9}

220 nF = 220 \times 1 0^{- 9} F

3In standard form:

2.2 \times 1 0^{- 7}

Answer

2.2 \times 1 0^{- 7}

Tip — Convert every prefixed quantity to plain SI units the moment you read it off the question, before you touch any equation — it removes an entire category of careless mistakes.

Equation recap

F = ma \Rightarrow N = kg m s^{- 2}

Deriving a unit from a defining equation (example: the newton).

Common mistakes to avoid

Substituting a value with its prefix still attached (e.g. using "220" for 220 nF) directly into a formula.

Always convert to the base SI unit first (220 nF = 2.2×10⁻⁷ F) before substituting into any equation.

Believing that if an equation is homogeneous, it must be entirely correct.

Homogeneity rules out dimensionally impossible equations, but says nothing about missing numerical factors like ½ or 2π.

Confusing "milli" (10⁻³) with "micro" (10⁻⁶) under time pressure.

These are three orders of magnitude apart — always double-check which prefix a question actually uses before converting.

Key takeaways

The six SI base units needed at A-Level are kg, m, s, A, K and mol.
Derived units (like N and J) come from a quantity’s defining equation, built from the base units.
Checking homogeneity (both sides reduce to the same base units) can disprove but never fully prove an equation.
SI prefixes (p, n, μ, m, c, k, M, G, T) must be converted to plain SI units before use in a calculation.

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SI Units, Prefixes and Homogeneity

30 min Video by Physics Online Module 2.1 Physical quantities and units