SI Base & Derived Units
Every measurement in physics is a number together with a unit. "The mass is 5" says nothing; "the mass is 5 kg" says exactly how much. Physical quantities are also tied to one another by formulas, and that saves a great deal of work: only a few units have to be chosen and defined, and every other unit can be built from them. The International System of Units, SI for short, chooses seven. This page is about those seven base units and about how the rest, the derived units, are built from them.
Units open the paper. Question 1 of every real paper so far has come from this topic. Two of them asked for an SI unit by name: the base unit of mass (January 2026, Q1) and the unit of force (March 2026, Q1). Both are worked through below. The other two asked whether a quantity is a vector or a scalar, which the next page teaches. None of these questions needs any arithmetic, and each takes about twenty seconds if you know one table. Their wrong options are real units of other quantities, so this page also builds a map on which every distractor has its place. It ends with a use for units in harder questions: an option with the wrong units cannot be the answer.
Seven base units
A base unit is defined directly, by a standard of measurement, and is not built from other units. The SI picks seven base quantities and gives each one a base unit.
| Base quantity | Base unit | Symbol |
|---|---|---|
| length | metre | m |
| mass | kilogram | kg |
| time | second | s |
| electric current | ampere | A |
| temperature (thermodynamic temperature) | kelvin | K |
| amount of substance | mole | mol |
| luminous intensity | candela | cd |
Mechanics needs only the first three. Every unit of motion, force and energy in this course is built from the metre, the kilogram and the second, which is why Chinese textbooks call these three the base units of mechanics (力学单位制, the mechanical system of units). The ampere joins them for electricity and the kelvin for heat. The mole counts particles and is used mainly in chemistry, and the candela measures how bright a light source looks to the eye. No physics paper so far has asked about either, but they complete the seven.
Units named after scientists are written with a small letter when spelled out and with a capital letter as a symbol: the ampere is A, the kelvin is K, and the newton, which comes later on this page, is N. A capital letter therefore tells you that a person's name is behind the unit, not whether it is a base unit.
Two details catch students out. First, the base unit of mass is the kilogram, not the gram. It is the only base unit whose name already contains a prefix: kilo- means a thousand, so 1 kg = 1000 g. When the metric system was set up in the 1790s, a gram was too small to make a practical standard, so the standard that was made was a kilogram, and the prefixed name stayed. A mass given in grams must therefore be changed to kilograms before it goes into a formula, which the Unit Conversions in Problems page practises.
Second, mass and weight have different units. Mass is the amount of matter in an object and is measured in kilograms. Weight is a force, the pull of the Earth on that matter, and is measured in newtons. You will meet the link between them, G = mg, in Weight, Springs & Friction: a 2 kg bag weighs 2 × 10 = 20 N on Earth. So N is the right answer when a question asks for the unit of weight, and a wrong one when it asks for the unit of mass.
The kilogram since 2019
A base unit needs a standard that everyone can compare against. For 130 years the kilogram's standard was a single object: a small cylinder of platinum and iridium, the International Prototype of the Kilogram, kept in a vault at the International Bureau of Weights and Measures near Paris. Its mass was 1 kg by definition, and every balance in the world was traced back to it through a chain of official copies.
An object makes a fragile standard. It can be scratched or pick up dirt, and it can be in only one laboratory at a time. Over a century of careful comparisons, the prototype and its official copies drifted apart by roughly 50 micrograms, and nobody could say which of them had changed, because the prototype was exactly 1 kg by definition, whatever happened to it. So the definition was moved from an object to a constant of nature, the Planck constant h, which has the same value everywhere and at every time. It comes from the physics of atoms and light, and you need nothing more about it here.
In November 2018 the General Conference on Weights and Measures, meeting for the 26th time, voted to fix h at exactly 6.62607015 × 10⁻³⁴ joule-seconds and to define the kilogram from it. The ampere, the kelvin and the mole were redefined from fixed constants in the same vote. The new definitions came into force on 20 May 2019. How fixing a constant can define a unit is shown in the next section, once derived units are in place.
For the exam, one fact matters: the kilogram's place in the system did not change. It has the same size as before, so no mass had to be measured again, and it is still the SI base unit of mass. Only the way it is defined is new.
The 26th International Conference on Weights and Measures decided to redefine the basic unit of mass, which came into effect on May 20, 2019. The basic unit of mass is
A. N B. s C. m D. kg
Step 1, strip the stem: the conference, its number and the date are history. They describe the redefinition, but they cannot change the answer, because the kilogram kept its place. "Basic unit" is the paper's translation of 基本单位, a base unit. The question is simply: what is the SI base unit of mass?
Step 2, recall: the base unit of mass is the kilogram. The answer is D.
A, N, is the newton, the unit of force, and so of weight. It is the trap for students who mix up mass and weight. B, s, and C, m, are base units, but of time and of length. Every option is a real SI unit, so the question tests whether you can match each unit to its quantity.
Derived units from their formulas
Every other unit is built from the base units, and the recipe is always the same: take the formula that defines the quantity, and put in the units of the quantities on its right-hand side. Start with motion. Velocity is displacement divided by time, v = Δx/Δt, so its unit is the metre divided by the second, m/s. Acceleration is the change of velocity divided by time, a = Δv/Δt, so its unit is (m/s) ÷ s = m/s². You will meet both definitions in Describing Motion.
Force comes next. Newton's second law, F = ma, which you will meet in Newton's Laws, multiplies a mass by an acceleration, so the unit of force is kg × m/s² = kg·m/s². This combination is used so often that it has a name of its own, the newton: 1 N = 1 kg·m/s². In words, 1 N is the net force that gives a 1 kg mass an acceleration of 1 m/s². A named unit is only a short name for a combination of base units; it needs no new standard.
The same recipe gives the rest of mechanics. Work is force times distance, W = Fs, so its unit is N·m, named the joule: 1 J = 1 N·m = 1 kg·m²/s². Power is work done per second, P = W/t, so its unit is J/s, named the watt: 1 W = 1 J/s = 1 kg·m²/s³. Pressure is force per unit area, p = F/S, so its unit is N/m², named the pascal: 1 Pa = 1 N/m². You will meet work and power in Work & Energy.
Two more units complete the mechanics set. Frequency is the number of cycles per second, f = 1/T, so its unit is 1/s = s⁻¹, named the hertz (Hz); you will meet it in Oscillations & Waves. Momentum is mass times velocity, p = mv, with unit kg·m/s, and impulse is force times time, I = Ft, with unit N·s. These two must agree, because an impulse changes a momentum, and they do: N·s = (kg·m/s²) × s = kg·m/s. You will meet both in Momentum & Impulse.
In the International System of Units (SI), the unit of force is ( ).
A. Ohm (Ω) B. Newton (N) C. Watt (W) D. Joule (J)
The formula that defines force is F = ma, so its unit is kg·m/s², which is named the newton. The answer is B.
The other three are real units, each of another quantity. D, the joule, is N·m, the unit of work and energy: a force times a distance. C, the watt, is J/s, the unit of power: work per second. Both are built on the newton, which is why they sit beside it in the options. A, the ohm, is the unit of electrical resistance, which you will meet in DC Circuits; it is in the table further down this page.
Electric and magnetic units, for reference
The papers mix units from electricity and magnetism into their options, as March's ohm did. The same recipe builds all of them, and the only new ingredient is the fourth base unit, the ampere. Notice which way round it goes: current, not charge, is the base quantity. Charge is current multiplied by time, q = It, so the coulomb is a derived unit, 1 C = 1 A·s.
Each quantity in the table is defined in a later topic, and you do not need the definitions yet. What the table gives you now is a place for every unit an option might show, so that a distractor such as the ohm or the tesla is never a mystery.
| Quantity | Defined by | SI unit |
|---|---|---|
| electric current I | a base quantity | ampere, A |
| electric charge q | q = It | coulomb: 1 C = 1 A·s |
| voltage (potential difference) U | U = W/q | volt: 1 V = 1 J/C |
| resistance R | R = U/I | ohm: 1 Ω = 1 V/A |
| electric field strength E | E = F/q | newton per coulomb, N/C (the same as V/m) |
| magnetic flux density B | B = F/(IL) | tesla: 1 T = 1 N/(A·m) |
| magnetic flux Φ | Φ = BS | weber: 1 Wb = 1 T·m² |
Read each row the way you read the mechanics units. The volt is a joule per coulomb because a voltage is the energy transferred per unit of charge; the ohm is a volt per ampere because resistance is the voltage needed per unit of current. You will meet charge in Charge & Coulomb's Law, the volt and the ohm in DC Circuits, E in Electric Field & Potential, and B and Φ in Magnetic Fields & Forces. Two papers have already asked for the units of B and Φ (December 2025, Q30; April 2026, Q29). That question is worked through on the second page of Magnetic Fields & Forces, where B and Φ are defined.
Checking an option by its units
Units do more than answer Q1. The two sides of an equation describe the same quantity, so they must have the same units. When the options of a question are formulas, any option whose units do not match the quantity asked for cannot be right, whatever the physics. The check takes a few seconds, and it is worth doing before any long derivation.
Your turn! · Practice questions
Things to remember
| Concept | What to know |
|---|---|
| Base units | Seven: m (length), kg (mass), s (time), A (electric current), K (temperature), mol (amount of substance), cd (luminous intensity). Mechanics uses only m, kg and s. |
| The kilogram | The base unit of mass is the kilogram, not the gram. Since 20 May 2019 it has been defined by fixing the Planck constant instead of by a metal cylinder; its size did not change. January 2026 Q1: kg. |
| Mass and weight | Mass is in kg. Weight is a force, in N. N is the trap when the unit of mass is asked. |
| Building a derived unit | Write the defining formula, put in the units of the quantities on the right, and simplify. |
| Mechanics units | N = kg·m/s² (F = ma), J = N·m (W = Fs), W = J/s (P = W/t), Pa = N/m² (p = F/S), Hz = s⁻¹ (f = 1/T), N·s = kg·m/s (impulse and momentum). March 2026 Q1: the newton. |
| Electric and magnetic units | The ampere is a base unit. C = A·s, V = J/C, Ω = V/A, N/C = V/m, T = N/(A·m), Wb = T·m². |
| Look-alikes | N is a force, J = N·m is an energy, W = J/s is a power. The letter W is the work in P = W/t but the watt as a unit. The pascal divides a force by an area. |
| Long stems | History in the stem (a conference, a date, a constant) does not change the answer. "Basic unit" means base unit (基本单位). |
| Units check | Both sides of an equation have the same units. Reduce the target and each option to base units and cross out the mismatches: mgt is a momentum, not a power (January 2026 Q41); a q–t slope is in amperes, so only U/R fits (March 2026 Q26). |