The International System of Units (SI)

Introduction

There are thousands of things scientists measure — speed, pressure, energy, concentration, radioactivity — yet every one of them can be expressed using just seven basic units. This is the elegant idea behind the International System of Units, known everywhere by its French initials SI (Système international d'unités). Learn the seven base units and you hold the key to every unit you will meet in chemistry.

Core explanation

Seven base quantities. SI chooses seven quantities that are treated as independent of each other. Each has one base unit:

Base quantity Unit name Unit symbol --- --- --- Length metre m Mass kilogram kg Time second s Electric current ampere A Thermodynamic temperature kelvin K Amount of substance mole mol Luminous intensity candela cd

For chemists, the most used are the metre, kilogram, second, kelvin and mole. The ampere matters in electrochemistry, and the candela mainly in the study of light and vision.

Derived units. Every other SI unit is made by multiplying or dividing base units. Area is length × length, so its unit is m². Volume is m³. Speed is length ÷ time, m/s. Density is mass ÷ volume, kg/m³. Some derived units have special names for convenience: the newton (N) for force is kg m/s², and the joule (J) for energy is kg m²/s². Behind the name, they are still combinations of base units.

Prefixes. Base and derived units can be made larger or smaller using prefixes that stand for powers of ten, such as kilo (10³), centi (10⁻²) and milli (10⁻³). So 1 km = 1000 m and 1 mg = 0.001 g. Prefixes are covered in detail later in this unit.

How SI is defined today. Since 2019, the seven base units have been defined by fixing the exact numerical values of seven constants of nature. For example, the speed of light in vacuum is fixed at exactly 299 792 458 m/s, which defines the metre once the second is defined. The Avogadro constant is fixed at exactly 6.022 140 76 × 10²³ per mole, which defines the mole. Because the constants never change, the units never drift.

Writing SI correctly. Unit symbols are written in upright type and are case-sensitive: m (metre) is not M, and K (kelvin) is not k (the prefix kilo). Symbols named after people start with a capital letter (A, K, N, J), but the full names are written in lower case (ampere, kelvin, newton). There is no full stop after a symbol unless it ends a sentence, and no plural "s".

Step-by-step reasoning

To find the SI unit of any quantity:

1. Write the defining equation, for example density = mass ÷ volume. 2. Replace each quantity with its SI unit: kg ÷ m³. 3. Simplify to get the derived unit: kg/m³ (also written kg m⁻³). 4. Check whether the combination has a special name, such as newton or joule.

Visual explanation

Imagine seven building blocks of different colours, each labelled with a base unit. Derived units are small models built by stacking these blocks: two "m" blocks make m², three make m³, and a "kg" block over three "m" blocks makes kg/m³. Every unit in science is a model built from the same seven blocks.

Real-world analogy

The seven base units are like the primary ingredients in a kitchen: flour, eggs, sugar and so on. From a small set of ingredients a cook can make hundreds of dishes. In the same way, a few base units combine to make every unit in science.

Real-world example

A car's fuel efficiency, a medicine's concentration and an electricity bill all rest on SI. Electricity companies charge per kilowatt-hour, a unit of energy that can be traced back to the kilogram, metre and second. Because the base units are shared internationally, meters and scales can be checked against national standards.

Why?

Why only seven base units? Because keeping the base set small and independent avoids contradictions. If there were many unconnected units, converting between them would require endless tables. With seven, every other unit follows logically, and an equation's units can always be checked by breaking them down into base units.

Common misconception

"The gram is the SI base unit of mass." The base unit is the kilogram. The gram is a smaller unit formed with a prefix. Similarly, the base unit of temperature is the kelvin, not the degree Celsius, and the litre is not an SI unit at all, although it is accepted for use with SI.

Worked example

Question: Pressure is defined as force ÷ area. Force is measured in newtons (kg m/s²). Find the SI unit of pressure in base units.

Reasoning: Area has unit m². Pressure = (kg m/s²) ÷ m² = kg/(m s²).

Answer: kg m⁻¹ s⁻², which is given the special name pascal (Pa).

Quick check

1. Which SI base unit is used for amount of substance? Answer: The mole, symbol mol.

Exam focus

Learn the table of seven base quantities, units and symbols — it is frequently tested. Watch the capital letters: K for kelvin, A for ampere, and lower-case m, kg, s, mol and cd. You may be asked to express a derived unit in base units.

Advanced insight

The 2019 redefinition fixed seven constants: the caesium hyperfine frequency, the speed of light, the Planck constant, the elementary charge, the Boltzmann constant, the Avogadro constant and the luminous efficacy of a specific green light. Every SI unit can now be realised from these values, making SI truly universal — in principle, even another civilisation could reproduce it.

Summary

SI has seven base units: metre, kilogram, second, ampere, kelvin, mole and candela. All other units are derived by multiplying and dividing them, and some derived units have special names such as newton and joule. Prefixes scale units by powers of ten. Since 2019, the base units are defined by fixed constants of nature.

Practice questions

1. List the seven SI base units with their symbols. Answer: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd). 2. What is the SI unit of volume? Answer: The cubic metre, m³. 3. Speed is distance ÷ time. Give its SI unit. Answer: m/s (metres per second), also written m s⁻¹. 4. Why is it wrong to write the kelvin symbol as "k"? Answer: Symbols are case-sensitive; "k" is the prefix kilo, while the kelvin symbol is capital K. 5. Is the litre an SI unit? Explain. Answer: No; it is a non-SI unit accepted for use with SI, equal to one cubic decimetre (dm³).