SI Units

Imagine every country using its own units — a French chemist measuring in one set, a Japanese engineer in another, an American physicist in a third. Sharing a result would mean a page of conversions before anyone could even begin. So scientists everywhere agreed to speak one language of measurement: the Système International d'unités, or SI for short. When you write a length in metres or a mass in kilograms, you are using the same units as every laboratory on Earth (and every spacecraft above it).

The clever part is how small the system is. From just seven carefully chosen base units, every other scientific unit — for speed, force, energy, power, pressure, voltage and hundreds more — is built by combining them. Learn the seven, and you hold the key to all the rest.

A measurement is a number and a unit

Before the units themselves, one idea underpins everything. A measurement is never just a number. Written properly it is always a number multiplied by a unit:

\text{measurement} = \text{number} \times \text{unit}

"The bag is 5" tells you nothing — 5 grams? 5 kilograms? 5 tonnes? But 5\ \text{kg} is a real, complete answer that means exactly the same thing to everyone. The number says how many, and the unit says how many of what. Drop the unit and the number is meaningless. This is the habit that makes measuring in science trustworthy — the same care you met when measuring in science.

The seven SI base units

These seven are the foundation stones. Each one measures a different physical quantity — a different kind of thing about the world — and each has an agreed unit with a short symbol. You will use the first three (metre, kilogram, second) constantly; the others appear as you meet electricity, heat, chemistry and light.

Length — the metre (\text{m}): how long, wide or tall something is.
Mass — the kilogram (\text{kg}): how much stuff (matter) is in it.
Time — the second (\text{s}): how long something takes.
Electric current — the ampere (\text{A}): how fast charge flows.
Temperature — the kelvin (\text{K}): how hot or cold something is.
Amount of substance — the mole (\text{mol}): how many particles (atoms or molecules) there are.
Luminous intensity — the candela (\text{cd}): how bright a light source is.

That's the whole foundation — seven units for seven quantities. Everything else in physics is assembled from these.

Six of the seven base units have plain one-word names, but the mass unit is the kilogram — a word that already contains a prefix, "kilo" (meaning a thousand). It looks like a mistake, as if the base unit "should" be the gram. It isn't: by international agreement the kilogram is the base unit, and the gram is just \tfrac{1}{1000} of it. It's a historical quirk — when the system was set up, the practical standard lump of metal happened to have a mass of about one kilogram, so that became the base. Handy to know when someone tries to catch you out with "the gram is a base unit" — it isn't.

Derived units: building the rest from the seven

A derived unit is one you make by multiplying and dividing base units together. You have already met one without noticing: speed. Speed is a distance divided by a time, so its unit is a length unit divided by a time unit:

\text{speed} = \frac{\text{distance}}{\text{time}} \quad\Longrightarrow\quad \text{unit} = \frac{\text{m}}{\text{s}} = \text{m/s}.

No new letter needed — \text{m/s} is simply "metres per second". Many derived units are so useful that they get their own special name, but every one still traces back to the base units underneath.

Worked example — the newton (force). Newton's second law says force equals mass times acceleration, F = ma. Acceleration is measured in \text{m/s}^2 (metres per second, per second). So:

[\,F\,] = \text{kg} \times \frac{\text{m}}{\text{s}^2} = \frac{\text{kg}\cdot\text{m}}{\text{s}^2}.

This bundle of base units is used so often that it earns the name newton (\text{N}). One newton is the force needed to accelerate one kilogram at one metre per second squared — 1\ \text{N} = 1\ \text{kg}\cdot\text{m/s}^2. (It is roughly the weight of a small apple resting in your hand.)

Worked example — the joule (energy). The energy transferred, or work done, is force times the distance moved, W = F \times d. So its unit is a newton times a metre:

[\,W\,] = \text{N} \times \text{m} = \text{N}\cdot\text{m} = \frac{\text{kg}\cdot\text{m}^2}{\text{s}^2}.

That earns the name joule (\text{J}). Notice how it peels apart: a joule is a newton-metre, and a newton is \text{kg}\cdot\text{m/s}^2, so a joule is \text{kg}\cdot\text{m}^2/\text{s}^2 — pure base units all the way down.

Worked example — the watt (power). Power is how fast energy is transferred — energy divided by time, P = W/t. So:

[\,P\,] = \frac{\text{J}}{\text{s}} = \frac{\text{kg}\cdot\text{m}^2}{\text{s}^3}.

That is the watt (\text{W}): one joule of energy moved every second. A phone charger is a few watts; a kettle is a couple of thousand.

Try it: take a unit apart

Here is the idea made interactive. Pick a quantity below and watch its unit break down into the three mechanical base units — kilogram, metre and second. The exponent under each tile tells you how many times that base unit is multiplied in (a positive power) or divided out (a negative power). Read the row of tiles left-to-right and you rebuild the formula at the top.

Every quantity you can pick — force, energy, power, pressure — is nothing more than kilograms, metres and seconds combined in different amounts. That is the whole point of SI: a handful of base units, endlessly recombined.

Why a shared system matters

Agreeing on units isn't bureaucratic fussiness — it lets scientists on opposite sides of the planet compare results, repeat each other's experiments, and trust the numbers. A discovery in one lab means exactly the same thing in every other. Get it wrong, and the consequences can be spectacular.

In 1999 NASA's Mars Climate Orbiter arrived at Mars after a journey of hundreds of millions of kilometres — and promptly vanished. The cause was a units blunder. One team's software calculated the spacecraft's thruster nudges in pounds-force (an imperial unit), while the navigation software expected them in newtons (the SI unit) — and nobody had checked. A newton is only about a fifth of a pound-force, so every number was the wrong size. The orbiter dipped far too low into the Martian atmosphere and was torn apart, a loss of well over £100 million. Had both teams simply used SI units, the mission would almost certainly have survived. It is the most expensive units mistake in history — and a permanent reminder of why everyone uses the same system.

Three traps catch nearly everyone out with SI units.

A quantity is not a unit. Mass is the quantity (the thing you're measuring); the kilogram is its unit (what you measure it in). "How heavy?" is a quantity; "3 kg" is a measurement of it. Keep the two words apart.
The base unit of mass is the kilogram, not the gram. It's the one base unit whose name carries a prefix, so it looks like the odd one out — but by definition the kilogram is the base, and the gram is one-thousandth of it.
A derived unit is still made of base units. The newton, joule and watt have their own special names, but that doesn't make them new "basic" units — each one unpacks completely into kilograms, metres and seconds (\text{N} = \text{kg}\cdot\text{m}/\text{s}^2, and so on).

For over a century, the kilogram was defined by an actual object: a shiny cylinder of platinum-iridium alloy locked in a vault near Paris, known as Le Grand K. By international agreement, its mass simply was one kilogram — every set of scales on Earth ultimately traced back to that one lump. The trouble is that a physical object can change: over the decades Le Grand K drifted very slightly in mass compared with its official copies, by a few tens of micrograms. A universe-wide standard that quietly changes is a serious problem.

So in 2019 the world's scientists retired the lump. The kilogram is now defined using a fixed value of the Planck constant — a fundamental constant of nature that is the same everywhere in the universe and can never tarnish, drift or be dropped. Any properly equipped laboratory can now realise the kilogram from the constant itself. The other base units got the same treatment: the metre is defined by the speed of light, the second by the vibration of a caesium atom. SI is no longer anchored to any single object — it is anchored to the constants of the cosmos.