SI Units

SI Base Units

Imagine trying to buy a "handful" of apples or a "short walk" of wire—without a standard system of measurement, sharing scientific discoveries globally would be impossible. To ensure consistency, scientists use the International System of Units (SI Units).

At the core of this system is the base unit, which is a fundamental, absolute unit of measurement that cannot be mathematically broken down into simpler units. For Edexcel GCSE Physics, you must recall six primary physical quantities and their SI base units:

Physical Quantity	SI Base Unit	Unit Symbol
Mass	kilogram	kg
Length	metre	m
Time	second	s
Electric Current	ampere	A
Temperature	kelvin	K
Amount of Substance	mole	mol

Notice the strict rules for capitalisation. The full name of any unit is always written entirely in lowercase (e.g., newton, ampere, kelvin). However, the abbreviation symbol is capitalised only if the unit is named after a person (e.g., A for Ampere, K for Kelvin). Symbols not named after people remain lowercase (e.g., m, kg, s).

Unit Prefixes and Standard Form

The universe contains scales ranging from the microscopic width of an atom to the vast distance between galaxies. To handle very large or small numbers without writing endless zeros, scientists use unit prefixes and standard form.

Standard form expresses numbers as $A \times 10^n$, where $1 \le A < 10$. Prefixes act as standard multipliers to convert to and from base units. You must memorise the following standard prefixes:

• Giga (G): $\times 10^9$ (1,000,000,000)
• Mega (M): $\times 10^6$ (1,000,000)
• Kilo (k): $\times 10^3$ (1,000)
• Centi (c): $\times 10^{-2}$ (0.01)
• Milli (m): $\times 10^{-3}$ (0.001)
• Micro ($\mu$): $\times 10^{-6}$ (0.000001)
• Nano (n): $\times 10^{-9}$ (0.000000001)

Note: Mass is the only physical quantity where the SI base unit (kilogram) already includes a prefix.

Worked Example: Prefix Conversion

A current is given as $0.1 \mu\text{A}$. Express this in standard SI base units.

• Step 1: Identify the multiplier for the prefix. $\mu = 10^{-6}$.

• Step 2: Multiply the value by the prefix multiplier.

• Step 3: $0.1 \times 10^{-6} = 1 \times 10^{-7}\text{ A}$.

Derived SI Units

You can snap a piece of chalk, but try snapping a diamond—describing the physical differences between materials requires combining foundational measurements. A derived unit is obtained by the mathematical multiplication or division of one or more base units.

Many derived units are given "special names" to honour famous scientists. You must be able to recall these derived units and understand how they relate to base units:

Physical Quantity	Derived Unit	Symbol	Base Equivalent / Derivation
Frequency	hertz	Hz	$1/\text{s}$ or $\text{s}^{-1}$
Force	newton	N	$\text{kg m/s}^2$ (from $F = ma$)
Energy / Work	joule	J	$\text{N m}$ or $\text{kg m}^2/\text{s}^2$ (from $W = Fd$)
Power	watt	W	$\text{J/s}$ or $\text{kg m}^2/\text{s}^3$ (from $P = E/t$)
Pressure	pascal	Pa	$\text{N/m}^2$ or $\text{kg m}^{-1}\text{s}^{-2}$ (from $P = F/A$)
Electric Charge	coulomb	C	$\text{A s}$ (from $Q = It$)
Potential Difference	volt	V	$\text{J/C}$ or $\text{W/A}$ (from $V = E/Q$)
Electrical Resistance	ohm	$\Omega$	$\text{V/A}$ (from $V = IR$)
Magnetic Flux Density	tesla	T	(Specific to Higher Tier)

Other common derived units do not have special names. For example, the units for specific heat capacity are $\text{J/kg }^\circ\text{C}$ (or $\text{J/kg K}$), and specific latent heat is measured in $\text{J/kg}$.

Worked Example: Deduce the Base Units ("Show that")

Deduce the SI base units for Force.

• Step 1: State the relevant fundamental equation: $F = ma$.

• Step 2: Substitute the known base units for mass ($\text{kg}$) and acceleration ($\text{m/s}^2$).

• Step 3: Combine to show that $1\text{ N} \equiv \text{kg m/s}^2$.

Non-Standard Conversions

Every time you boil a kettle for exactly three minutes, you are using a measurement of time that physics equations cannot process directly. Values often appear in exams in non-standard units and must be manually converted before calculating.

• Time: Minutes or hours must be converted to seconds. Multiply hours by 3600 ($1\text{ hour} = 3600\text{ s}$).
• Temperature: To convert Celsius ($^\circ\text{C}$) to Kelvin (K), add 273. The formula is $T(\text{K}) = \theta(^\circ\text{C}) + 273$.
• Density: To convert density from $\text{g/cm}^3$ to standard SI units of $\text{kg/m}^3$, multiply the value by 1000.

Worked Example: Complex Conversion

Calculate the wavelength of a wave with a frequency of $6\text{ MHz}$ and speed of $3 \times 10^8\text{ m/s}$.

• Step 1: Convert non-standard units to base units. $6\text{ MHz} = 6 \times 10^6\text{ Hz}$.

• Step 2: Rearrange the wave equation ($\lambda = v / f$) and substitute values.

• Step 3: $\lambda = (3 \times 10^8) / (6 \times 10^6) = 50\text{ m}$.