SI units, prefixes and standard form
AQA expects you to move fluently between base units, derived units, prefixes and standard form. These are small skills, but they decide marks across mechanics, electricity, waves, particles and fields.
1. Learn the language
Memorise the six AQA base units and the prefix powers. You should not need to hunt for these in a calculation.
2. Convert first
Before substituting into an equation, convert prefixes into powers of ten and write values in SI units.
3. Check the final unit
A sensible number with a wrong unit is still a lost mark. Use the unit to test whether the answer makes physical sense.
- state the AQA base quantities and units for mass, length, time, amount of substance, temperature and current;
- derive units such as N, J, W, Pa, C and V from equations;
- use the prefixes T, G, M, k, c, m, µ, n, p and f without mixing powers of ten;
- convert values into standard form before using them in calculations;
- convert between J and eV, and between J and kWh.
The six base units AQA expects
Base units are the building blocks for the units used in physics. The candela is a base SI unit in the wider SI system, but AQA says light intensity is excluded for this specification.
| Quantity | SI unit | Symbol | Exam trap |
|---|---|---|---|
| Mass | kilogram | kg | kg is the base unit, not g. |
| Length | metre | m | Do not leave cm or mm inside equations. |
| Time | second | s | Convert minutes and hours unless the unit is deliberately kWh. |
| Amount of substance | mole | mol | Use mol, not moles, in unit algebra. |
| Temperature | kelvin | K | Temperature difference in K has the same size as in degrees Celsius. |
| Electric current | ampere | A | mA and µA must be converted before using circuit equations. |
You are not expected to recall formal definitions of the base quantities, and dimensional analysis is not required. You do need to recognise and use the units accurately.
Derived units come from equations
A derived unit is made by combining base units. The cleanest method is to start from a familiar equation, replace each quantity with its unit, and simplify the powers.
Force
Use F = ma.
The newton is a shorthand for base units.
Energy
Use E = 1/2 mv2.
The factor 1/2 has no unit.
Power
Use P = E/t.
One watt is one joule per second.
Potential difference
Use V = E/Q and Q = It.
This is why voltage units can look complicated in base units.
Prefixes are powers of ten attached to units
Convert the prefix before substituting. The symbol is case-sensitive: M means mega, but m means milli.
Area and volume conversions square or cube the conversion factor. For example, 1 cm2 = (10-2 m)2 = 10-4 m2, not 10-2 m2.
A reliable conversion routine
Step 1
Replace the prefix with its power of ten.
Step 2
Put the number into standard form if needed.
Step 3
Only then substitute into the physics equation.
J, eV and kWh
AQA specifically names conversions between joules and electronvolts, and between joules and kilowatt-hours. Treat both as energy units, not as separate topics.
Electronvolt
One electronvolt is the energy transferred when an electron moves through a potential difference of 1 V.
Example: 2.5 MeV = 2.5 x 106 x 1.60 x 10-19 = 4.0 x 10-13 J.
Kilowatt-hour
A kilowatt-hour is the energy transferred by a power of 1 kW for 1 hour.
Example: 0.75 kWh = 0.75 x 3.6 x 106 = 2.7 x 106 J.
Can you convert before calculating?
Choose the correct conversion or derived unit. These are the types of small decisions that often sit inside longer AQA questions.
Exam-style examples
1. Capacitance with a prefix
A capacitor has capacitance 220 µF and potential difference 12 V. Calculate the charge stored.
C = 220 x 10-6 F, so Q = CV = 220 x 10-6 x 12 = 2.64 x 10-3 C.
2. Area conversion
A force of 48 N acts over an area of 3.0 cm2. Calculate the pressure.
3.0 cm2 = 3.0 x 10-4 m2, so p = F/A = 48 / (3.0 x 10-4) = 1.6 x 105 Pa.
3. Photon energy
A photon has energy 3.2 eV. Convert this to joules.
E = 3.2 x 1.60 x 10-19 = 5.12 x 10-19 J.
4. Electricity bill unit
A heater transfers 1.8 kWh of energy. Convert this to joules.
E = 1.8 x 3.6 x 106 = 6.48 x 106 J.
Self-check questions
1. Convert 56 nC into coulombs.
56 nC = 56 x 10-9 C = 5.6 x 10-8 C.
2. Convert 12 mm into metres.
12 mm = 12 x 10-3 m = 1.2 x 10-2 m.
3. Write the pascal in SI base units.
Pa = N m-2 = kg m s-2 m-2 = kg m-1 s-2.
4. Convert 9.6 x 10-13 J into eV.
E = (9.6 x 10-13) / (1.60 x 10-19) = 6.0 x 106 eV = 6.0 MeV.
Final checklist for AQA 3.1.1
- Use kg, m, s, mol, K and A as the six required base units.
- Convert prefixes before substituting into equations.
- Remember that M and m are different prefixes.
- Square or cube the whole conversion factor for area and volume.
- Use 1 eV = 1.60 x 10-19 J.
- Use 1 kWh = 3.6 x 106 J.
- Check that the final unit matches the quantity asked for.