Quantities and measurement

Use H1 Physics SI units and dimensional checks, estimate quantities, combine uncertainties and add or resolve vectors.

GCE A-Level H1 Physics 2027
3 lessons

Before you begin

Every result in physics is a number, a unit and an uncertainty, and some also need a direction. The lessons start with SI units and how to check an equation with them, then deal with estimates, errors and the uncertainty in a calculated result, and finish with adding and resolving vectors.

Be comfortable with: O-Level measurement, because this topic builds on physical quantities, units and reading instruments, and with powers of ten and basic trigonometry.

Learning goals

Use SI quantities, units, prefixes and dimensional analysis.
Estimate physical quantities and check the reasonableness of results.
Assess random, systematic and propagated uncertainties.
Resolve, add and subtract coplanar vectors.

Syllabus statements covered

recall and use the following SI base quantities and their units: mass (kg), length (m), time (s), current (A), temperature (K), amount of substance (mol)
recall and use the following prefixes and their symbols to indicate decimal sub-multiples or multiples of both base and derived units: pico (p), nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G), tera (T)
express derived units as products or quotients of the SI base units and use the named units listed in ‘Summary of Key Quantities, Symbols and Units’ as appropriate
use SI base units to check the homogeneity of physical equations
make reasonable estimates of physical quantities included within the syllabus
show an understanding of the distinction between random errors and systematic errors (including zero error) which limit precision and accuracy
assess the uncertainty in derived quantities by adding absolute or relative (i.e. fractional or percentage) uncertainties or by numerical substitution (rigorous statistical treatment is not required)
distinguish between scalar and vector quantities, and give examples of each
add and subtract coplanar vectors
represent a vector as two perpendicular components

Lessons

Work through them in order.

Practise and check

Or choose

Topic reference

Quick reference

Idea	Rule	Example
SI base units	kg, m, s, A, K, mol
derived units	write the defining equation in base units	N = kg m s⁻², J = kg m² s⁻²
prefixes	p 10⁻¹², n 10⁻⁹, μ 10⁻⁶, m 10⁻³, c 10⁻², d 10⁻¹, k 10³, M 10⁶, G 10⁹, T 10¹²	1 cm³ = 10⁻⁶ m³
homogeneity	every term in an equation has the same base units	v = u + at: every term in m s⁻¹
sum or difference	Δ q = Δ a + Δ b
product or quotient	(Δ q)/q = (Δ a)/a + (Δ b)/b
power q = aⁿ	(Δ q)/q = \|n\|(Δ a)/a	A = π r²: double the fractional uncertainty in r
components	Fₓ = F cos θ, Fy = F sin θ	θ measured from the x-axis
resultant	R = square root of (Rₓ² + Ry²), tan θ = Ry/Rₓ

Core knowledge to remember

The SI base quantities and units are mass (kg), length (m), time (s), current (A), temperature (K) and amount of substance (mol).
A homogeneous equation has the same base units in every term. A homogeneity check can show that an equation is wrong, but not that it is right.
Random errors scatter readings unpredictably and limit precision; averaging reduces them. Systematic errors, including zero errors, shift every reading the same way and limit accuracy; averaging does not remove them.
Precision is how close repeated readings are to each other. Accuracy is how close they are to the true value.
The uncertainty in a derived quantity is found by adding absolute uncertainties (sums and differences), adding fractional uncertainties (products, quotients and powers), or by numerical substitution.
A scalar has magnitude only; a vector has magnitude and direction. Vectors are added head to tail; subtracting a vector means adding its reverse.

Common mistakes

Converting cm² or cm³ with a factor of 10⁻² instead of squaring or cubing it.
Saying an equation is correct because it is homogeneous.
Thinking repeated readings remove a systematic error.
Subtracting uncertainties when quantities are subtracted.
Adding absolute uncertainties for a product or quotient, or forgetting to multiply by a power.
Quoting a value to more decimal places than its uncertainty.
Adding the magnitudes of vectors that point in different directions.