"Seven basic units of measurement" is searched by students in grade 6 to 8 science and CBSE Class 6 meeting measurement for the first time, by Class 11 and AP Physics students revising units and dimensions, and by parents helping with a worksheet. The seven are the base units of the International System of Units (SI), and everything else in science is measured in combinations of them. This page lists the seven with what each measures and how it is defined, the derived units a school course uses and what they are built from, the prefixes, the rules for writing symbols that examiners mark, where the topic sits in each curriculum, and the mistakes that cost marks. The printable has all of it on two pages.
Download the SI units sheet (PDF) (the seven base units with definitions, the derived units in base-unit form, the prefix table, the symbol rules, and ten practice questions with answers; two pages, free).
The seven base units
| Quantity | Unit | Symbol | What it measures | How it is defined (since 2019) |
|---|---|---|---|---|
| Length | metre | m | Distance, height, width, wavelength | The distance light travels in a vacuum in 1/299,792,458 of a second (the speed of light is fixed at 299,792,458 m/s) |
| Mass | kilogram | kg | The amount of matter in an object (not its weight, which is a force) | From the Planck constant, fixed at 6.626 070 15 × 10⁻³⁴ J·s; until 2019 it was a platinum-iridium cylinder in Paris |
| Time | second | s | Duration | 9,192,631,770 periods of the radiation from a transition in the caesium-133 atom |
| Electric current | ampere | A | The flow of electric charge | From the elementary charge, fixed at 1.602 176 634 × 10⁻¹⁹ coulombs |
| Temperature | kelvin | K | Thermodynamic temperature, from absolute zero | From the Boltzmann constant, fixed at 1.380 649 × 10⁻²³ J/K; 0 K is absolute zero, 273.15 K is 0 °C |
| Amount of substance | mole | mol | A counted number of particles (atoms, molecules, ions) | Exactly 6.022 140 76 × 10²³ particles (the Avogadro constant) |
| Luminous intensity | candela | cd | The brightness of a light source in a given direction, as the eye sees it | From a fixed luminous efficacy of 683 lumens per watt at a frequency of 540 × 10¹² Hz |
Three things to notice. The kilogram is the only base unit with a prefix in its name (the gram is a thousandth of it, not the other way round). The kelvin has no degree sign and is not written "degrees kelvin". And since 2019 none of the seven depends on an object: each is tied to a constant of nature, so a laboratory anywhere can realise it.
The derived units a school course uses
Every other unit is a product or quotient of base units. The ones with their own names are the ones exams ask about, and the question is usually "express it in base units".
| Quantity | Unit | Symbol | In other units | In base units |
|---|---|---|---|---|
| Area | square metre | m² | m² | |
| Volume | cubic metre | m³ | 1 m³ = 1,000 litres | m³ |
| Speed | metre per second | m/s | m·s⁻¹ | |
| Acceleration | metre per second squared | m/s² | m·s⁻² | |
| Force | newton | N | kg·m·s⁻² | |
| Pressure | pascal | Pa | N/m² | kg·m⁻¹·s⁻² |
| Energy, work | joule | J | N·m | kg·m²·s⁻² |
| Power | watt | W | J/s | kg·m²·s⁻³ |
| Frequency | hertz | Hz | 1/s | s⁻¹ |
| Electric charge | coulomb | C | A·s | A·s |
| Voltage | volt | V | W/A, J/C | kg·m²·s⁻³·A⁻¹ |
| Resistance | ohm | Ω | V/A | kg·m²·s⁻³·A⁻² |
| Density | kilogram per cubic metre | kg/m³ | kg·m⁻³ |
Units named after people (newton, pascal, joule, watt, hertz, coulomb, volt, ohm, kelvin, ampere) have a capital symbol and a lower-case name: 5 N of force, five newtons. The litre (L or l), the tonne (t), the hour and the degree Celsius are accepted for use with the SI but are not SI units.
The prefixes
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | 10⁹ | gigawatt, gigabyte |
| mega | M | 10⁶ | megajoule, megahertz |
| kilo | k | 10³ | kilometre, kilogram |
| hecto | h | 10² | hectare (10,000 m²) |
| deca | da | 10 | decametre (rare) |
| deci | d | 10⁻¹ | decilitre |
| centi | c | 10⁻² | centimetre |
| milli | m | 10⁻³ | millimetre, milligram, millisecond |
| micro | µ | 10⁻⁶ | micrometre, microgram |
| nano | n | 10⁻⁹ | nanometre, nanosecond |
Converting: move the decimal by the difference in the powers. 3.5 km = 3,500 m; 250 mL = 0.25 L; 0.004 s = 4 ms; 1 µm = 1,000 nm. A squared unit converts twice: 1 m² = 10,000 cm²; a cubed one three times: 1 m³ = 1,000,000 cm³ (which is why 1 litre, 1,000 cm³, is a thousandth of a cubic metre; the cubic feet and litres conversions are in what is a cubic foot).
The symbol rules examiners mark
- Symbols are not abbreviations: no full stop (5 kg, not 5 kg.), no plural (5 kg, not 5 kgs).
- Lower case unless named after a person: m, s, kg, mol; N, J, W, Pa, Hz, K, A. The litre is the exception, written L or l.
- A space between the number and the symbol (10 m), except for degrees of angle (90°) and percent (50%); °C is written with a space before the degree sign: 25 °C.
- Products with a dot or a space (N·m), quotients with a slash or a negative power (m/s or m·s⁻¹), never two slashes (m/s/s is wrong; m/s² is right).
- The unit name is lower case even when the symbol is capital: five newtons, 5 N.
- Prefix and unit are one word: kilometre, km; the only exception in practice is the kilogram, which is the base unit itself.
Where it sits in each curriculum
| Curriculum | Where |
|---|---|
| US grades 6 to 8 | Physical science: the metric system, base and derived units, conversions; the base units are often introduced as the "seven fundamental units" |
| CBSE | Class 6 Motion and Measurement of Distances (the standard units); Class 11 Physics Chapter 1 Units and Measurements (all seven, dimensional analysis, significant figures), a guaranteed question |
| GCSE and IGCSE | Combined and separate science: SI units and prefixes in every physics paper; "state the SI unit of…" questions |
| IB Physics and AP Physics | Topic 1 measurement: base and derived units, uncertainty, orders of magnitude |
| A-level Physics | Year 12: the seven base units, homogeneity of equations (dimensional checks) |
The six mistakes that cost marks
- Giving the gram as the base unit of mass. It is the kilogram.
- Writing "degrees kelvin" or °K. The kelvin is a unit like the metre: 300 K.
- Confusing mass and weight. Mass is in kilograms (a base quantity); weight is a force, in newtons, and changes with gravity.
- Expressing a derived unit wrongly in base units. The joule is kg·m²·s⁻², not kg·m·s⁻²; check by writing out the formula (energy = force × distance = kg·m·s⁻² × m).
- Converting squared and cubed units once instead of twice or three times. 1 m² is 10,000 cm², not 100.
- Treating the mole as a mass. It is a number of particles; the mass of a mole depends on the substance (18 g for water, 12 g for carbon-12).
Download the SI units sheet (PDF)
Where to get help
A 1-on-1 online science class with a tutor who holds a master's in physics, from grade 6 physical science to CBSE Class 11, GCSE, IGCSE, IB and AP Physics: units taught with the formulas they come from, conversions practised until automatic, and the exam board's own "state the unit" and dimensional questions from the first week. The recording and notes after every class, the same tutor all year, US$10 to $13 an hour. The physics page has the courses; the free 30-minute first class is a real lesson on this week's topic.
Questions parents ask
1What are the seven basic units of measurement?
2Why is the kilogram the base unit and not the gram?
3Is Celsius a basic unit?
4What is the difference between a base unit and a derived unit?
5How were the units redefined in 2019?
See how we teach this, 1-on-1 online →
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