SI units
Topic 1 is examined on both papers, Paper 1 and Paper 2, but never as a question of its own.
Its skills sit inside the calculations of every other topic: wavelengths and speeds on Paper 1, currents, pressures and energies on Paper 2.
In the 2023 to 2025 papers, units, prefixes, conversions and significant figures carried marks inside more than twenty Paper 1 calculations, and in many more on Paper 2.
A missing conversion or a wrong unit is one of the commonest ways to lose a mark on either paper, so this short topic pays back more than its size suggests.
The examples in this unit use equations from later topics.
Each one is printed in the question, as a Foundation paper prints it, so that you can concentrate on the units.
You learn each equation, and whether you must recall it, in its own topic.
What a unit is for
A measurement is a number and a unit.
"The length is 2.5" means nothing on its own: it could be 2.5 mm or 2.5 km, a difference of a million times.
The unit tells you what the number counts.
A shop that sells cloth "by the metre" and a scientist who measures a wavelength "in metres" are counting the same thing, so their numbers can be compared.
Scientists everywhere agree to use one set of units, the SI units (from the French Système International d'Unités, the International System of Units).
The system starts from a few base units.
Every other unit is built from them by multiplying and dividing.
Because every equation in physics is written for SI units, a calculation works only if every value goes in as an SI unit.
You need to recall and use the SI unit for physical quantities.
The lists below are the ones you need.
Base units
These six units are the foundations.
None of them can be made from the others.
Quantity
SI unit
Unit symbol
length
metre
m
mass
kilogram
kg
time
second
s
electric current
ampere
A
temperature
kelvin
K
amount of substance
mole
mol
Two of these need a comment.
The kilogram is the only base unit that already carries a prefix ("kilo"), so a mass in grams must be divided by 1000 to give kilograms.
The kelvin is the SI unit of temperature; you meet the kelvin scale in the particle model topic.
Temperature changes in this course are usually given in degrees Celsius, °C, and a change of 1 °C is the same size as a change of 1 K. The mole is used far more in chemistry than in physics.
Derived units with special names
Every other unit is a derived unit: it is made by combining base units.
Some derived units are used so often that they have their own names, usually the name of a scientist.
You need these:
Quantity
Unit
Abbreviation
Built from
frequency
hertz
Hz
per second, 1/s
force
newton
N
kg m/s²
energy
joule
J
N m (a newton moving through a metre)
power
watt
W
J/s (a joule per second)
pressure
pascal
Pa
N/m² (a newton per square metre)
electric charge
coulomb
C
A s (an ampere for a second)
electric potential difference
volt
V
J/C (a joule per coulomb)
electric resistance
ohm
Ω
V/A (a volt per ampere)
magnetic flux density
tesla
T
N/A m
The unit names are written with a small letter (newton, joule, watt), but the symbols of units named after people take a capital letter (N, J, W, Pa, Hz).
The capital matters: "m" is metre (or milli), "M" is mega.
You see why in the next section.
Other units you use every day in physics
Many units have no special name.
You simply write the combination:
- speed and velocity: metres per second, m/s
- acceleration: metres per second squared, m/s²
- gravitational field strength: newtons per kilogram, N/kg
- momentum: kilogram metres per second, kg m/s
- density: kilograms per cubic metre, kg/m³
- spring constant: newtons per metre, N/m
- moment of a force: newton metres, N m
- specific heat capacity: joules per kilogram degree Celsius, J/kg °C
- specific latent heat: joules per kilogram, J/kg
Building a unit from an equation
You never need to guess a unit.
Write the equation, then replace each quantity by its unit and do the same multiplying or dividing to the units.
- pressure = force normal to surface ÷ area of surface, so the unit is N ÷ m² = N/m². This is the pascal: 1 Pa = 1 N/m².
- potential difference = energy transferred ÷ charge moved, so the unit is J ÷ C = J/C. This is the volt: 1 V = 1 J/C.
- charge = current × time, so the unit is A × s = A s. This is the coulomb: 1 C = 1 A s.
- spring constant = force ÷ extension, so the unit is N ÷ m = N/m.
- work done = force × distance, so the unit is N × m = N m. This is the joule: 1 J = 1 N m.
The same method tells you when a unit is impossible.
Charge comes from multiplying current and time, so its unit cannot be A/s, which would mean dividing.
Work comes from multiplying force and distance, so its unit cannot be N/m.
Why mass and weight have different units
Mass is the amount of matter in an object, a base quantity measured in kilograms with a balance.
Weight is a force, the pull of gravity on that mass, measured in newtons with a newton meter.
A 2.0 kg bag of flour has a weight of about 20 N on Earth.
Saying "the bag weighs 2 kg" is fine in a shop and wrong in a physics answer.
The photograph shows the two instruments side by side: a balance measures the mass of a bag of flour, and a newton meter measures the weight of an identical bag by how far the bag stretches its spring.
The unit on the answer line
On the papers, the answer line usually prints the unit for you: force = .................. N.
Read it before you calculate.
If the line says kJ and your working is in J, you must convert your answer; if it says hours, your answer must be in hours.
Sometimes the line is blank with a separate unit .................. line, and the unit is then its own mark.
That mark is independent: you can earn it with the right unit even if your number is wrong.
- Physical quantity: a property that can be measured, written as a number and a unit.
- SI unit: a unit of the International System of Units, the agreed system scientists use, built from base units such as the metre, kilogram, second and ampere.
- Base unit: one of the six SI units (metre, kilogram, second, ampere, kelvin, mole) from which all the others are made.
- Derived unit: a unit made by multiplying or dividing base units, such as m/s, or the newton, kg m/s².
Which of these is the SI unit of electric charge?
☐ A ampere
☐ B coulomb
☐ C joule
☐ D volt
(1)
Answer: B coulomb is the only correct answer (1).
A, the ampere, is the unit of current, the rate at which charge flows.
C, the joule, is the unit of energy.
D, the volt, is the unit of potential difference, the energy transferred per unit of charge.
The potential difference across a component is found using potential difference = energy transferred ÷ charge moved.
Give the unit of potential difference in terms of joules and coulombs.
(1)
1. replace each quantity by its unit: joule ÷ coulomb = J/C (1)
Answer: J/C, a joule per coulomb.
This unit has its own name, the volt (V): 1 V = 1 J/C. A potential difference of 6 V means 6 J of energy is transferred for every coulomb of charge that moves.
The current in a torch lamp is 0.30 A. The torch is switched on for 50 s.
Calculate the charge that flows through the lamp.
Use the equation: charge = current × time.
State the unit.
charge = ..................
unit ..................
(3)
1. substitution: charge = 0.30 × 50 (1)
2. evaluation: charge = 15 (1)
3. unit: C (coulombs) (1), allow A s; the unit mark is independent
Answer: 15 C. "15 A/s", "15 J" or "15 Q" earns the first two marks but not the unit mark: Q is the symbol for charge, not its unit.
A force of 6.0 N stretches a spring by 0.12 m.
Use the equation: force exerted on a spring = spring constant × extension.
(i) Calculate the spring constant of the spring. (3)
(ii) State the unit of the spring constant. (1)
1. substitution: 6.0 = spring constant × 0.12 (1)
2. rearrangement: spring constant = 6.0 ÷ 0.12 (1)
3. evaluation: spring constant = 50 (1)
4. unit: force ÷ extension = N ÷ m = N/m (1)
Answer: (i) 50 (ii) N/m.
A spring constant of 50 N/m means 50 N is needed for each metre of extension, or 0.5 N for each centimetre.
When you are not sure of a unit, build it from the equation: write the equation, put the units in place of the quantities, and multiply or divide them as the equation does.
N ÷ m² gives the pascal and J ÷ C gives the volt.
Then check the unit printed on the answer line before you start, so your number is in the unit the line asks for.
- Writing the symbol of the quantity as its unit. Q is charge, P is power or pressure; the units are C, W and Pa. "15 Q" scores nothing for the unit.
- Wrong units for charge. Candidates have written J, W, Hz, A/s and mA/s. Charge = current × time, so the unit is C (or A s).
- Wrong units for pressure. N m², N/m and "P" are all wrong. Pressure = force ÷ area: Pa or N/m².
- Wrong units for work done. N/m is the unit of a spring constant. Work done = force × distance: J, or N m.
- Giving a mass in newtons or a weight in kilograms. Mass is in kg; weight is a force, in N.
- Ignoring the capital letter. MW (megawatt) and mW (milliwatt) differ by a factor of a thousand million.
Check your understanding
1. Which row of the table shows a quantity with its correct SI unit?
quantity
unit
☐ A
frequency
newton
☐ B
resistance
ohm
☐ C
pressure
joule
☐ D
charge
ampere
(1)
Total [1]
2. Draw one straight line from each quantity to its unit.
quantity: force, energy, magnetic flux density
unit: hertz, joule, newton, tesla, watt
(3)
Total [3]
3. Complete the sentence using words from the box.
amperes
coulombs
ohms
volts
watts
The current in a lamp is measured in ..................
and the potential difference across the lamp is measured in ..................
.
(2)
Total [2]
4. A battery moves a charge of 40 C around a circuit. The potential difference of the battery is 9.0 V.
Calculate the energy transferred.
Use the equation
energy transferred = charge moved × potential difference
State the unit.
energy transferred = ..................
unit ..................
(3)
Total [3]
5. A student uses charge = current × time to calculate the charge that flows in a circuit. She writes her answer as 12 A/s.
(a) State the correct unit of charge.
(1)
(b) Explain why A/s cannot be the unit of charge.
(2)
Total [3]
6. This question is about units built from equations.
(a) Density = mass ÷ volume.
Give the unit of density.
(1)
(b) A student writes the pressure under a box as 300 N m².
State the correct unit for this pressure.
(1)
Total [2]
7. A student says: "The mass of my bag is 50 N."
(a) Explain what is wrong with the student's statement.
(2)
(b) Name the instrument used to measure mass in a laboratory.
(1)
Total [3]
Answers
1. B resistance and ohm is the only correct answer (1)
- A: frequency is measured in hertz; the newton is the unit of force.
- C: pressure is measured in pascals; the joule is the unit of energy.
- D: charge is measured in coulombs; the ampere is the unit of current.
2. - force to newton (1)
- energy to joule (1)
- magnetic flux density to tesla (1)
- more than one line from a quantity scores 0 for that quantity
3. - amperes (1)
- volts (1)
- in this order only
4. - substitution: energy transferred = 40 × 9.0 (1)
- evaluation: energy transferred = 360 (1)
- unit: J (joules) (1), independent of the number
- award full marks for the correct answer with its unit without working
5. (a) C (coulomb) (1), allow A s
(b) an explanation linking
- charge is found by multiplying current and time, so the units are multiplied: A × s (1)
- A/s would mean a current divided by a time, which is not how charge is calculated (1)
6. (a) kg/m³ (1), allow g/cm³
(b) Pa or N/m² (1); do not accept N m² or N/m
7. (a) an explanation linking
- the newton is the unit of force (or weight), not of mass (1)
- mass is measured in kilograms (so the mass is about 5 kg), or the weight of the bag is 50 N (1)
(b) a balance (1); allow a top-pan balance or electronic balance; do not accept a newton meter