SI Units and the Language of Measurement

Chemistry is a quantitative science, and every quantitative statement needs a unit. Saying "the mass is 12" means nothing until you say 12 of what — grams, kilograms, pounds? The International System of Units (SI) solves this problem. It fixes seven base units. Every other unit of measurement in science can be built from these. This article introduces those seven base units. It shows how chemists combine them into derived units. Examples include units for volume, density, and pressure. It also explains why a single, universal system of measurement matters so much. This matters especially for reproducible science. Everything that follows in quantitative chemistry rests on this foundation. That includes Metric Prefixes and Unit Conversion, Density, Temperature Scales, and eventually the mole itself. Think of SI as a common language. Two chemists on opposite sides of the planet can use the same unit definitions. They can then reproduce each other's measurements exactly. That shared vocabulary makes chemistry a cumulative, checkable science. It matters more than any single formula.

Key takeaways

SI defines seven base units: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), candela (luminous intensity).
Chemistry leans heavily on five of these: meter, kilogram, second, kelvin, and mole.
Derived units are built from base units by multiplication/division — volume (m³), density (kg/m³), pressure (Pa = kg·m⁻¹·s⁻²), and energy (J = kg·m²·s⁻²).
Since 2019, all seven base units are defined by fixed physical constants (like the speed of light and the Planck constant), not by physical objects.
A number without a unit is not a measurement — it is meaningless in a chemical context.
Key idea: SI units give every physical quantity a unique, reproducible definition built from just seven independent building blocks.

The core insight

Every measurable quantity in chemistry can be expressed as a number multiplied by a combination of the seven SI base units — nothing more is needed.

The physical picture

Imagine trying to describe the size of a beaker of water to a colleague without any units — you could say "the beaker holds 250," but 250 what? Milliliters? Grams? Cubic centimeters? Without a unit, a measurement is just a bare number, disconnected from physical reality. SI solves this by choosing seven quantities — length, mass, time, electric current, temperature, amount of substance, and luminous intensity — that are treated as dimensionally independent. No one of these seven can be constructed from combinations of the other six. Every other physical quantity used in chemistry, from concentration to viscosity, is built by multiplying and dividing these seven. The table below shows the seven base units, their symbols, and the modern definitions that fix their exact size.

Quantity	Unit name	Symbol	Modern definition basis
Length	meter	m	distance light travels in a fixed fraction of a second
Mass	kilogram	kg	fixed value of the Planck constant, h
Time	second	s	fixed number of oscillations of a cesium-133 atom
Electric current	ampere	A	fixed value of the elementary charge, e
Temperature	kelvin	K	fixed value of the Boltzmann constant, kB
Amount of substance	mole	mol	fixed value of the Avogadro constant, NA
Luminous intensity	candela	cd	fixed luminous efficacy of monochromatic light

Chemistry uses five of these seven constantly (meter, kilogram, second, kelvin, mole), touches the ampere occasionally (electrochemistry), and almost never needs the candela. From these seven, chemists build derived units by combining exponents of the base units. Volume is length cubed (m³); density is mass divided by volume (kg/m³); force is mass times acceleration (kg·m·s⁻², named the newton, N); pressure is force per area (N/m² = Pa); energy is force times distance (N·m = J, the joule). Every derived unit in a chemistry course can be traced back, exponent by exponent, to the seven base units.

Figure

Figure 1 — The seven SI base units and how chemistry-relevant derived units are built from them

The core relations

The defining relationships of SI are not "equations" in the algebraic sense so much as dimensional definitions — statements of how a unit's size is fixed and how derived units are constructed. The essential relations chemists use constantly are:

1\ \text{L} = 1 \times 10^{-3}\ \text{m}^3 = 1000\ \text{cm}^3

where: L is the liter (a non-SI unit tolerated for volume), m³ is the SI-derived cubic meter, cm³ is the cubic centimeter.

\rho = \dfrac{m}{V}

where: $\rho$ is density (kg/m³ or g/cm³), $m$ is mass (kg or g), $V$ is volume (m³ or cm³).

T(\text{K}) = T(^{\circ}\text{C}) + 273.15

where: $T(\text{K})$ is absolute (kelvin) temperature, $T(^{\circ}\text{C})$ is Celsius temperature, 273.15 is the fixed offset between the two scales.

1\ \text{Pa} = 1\ \dfrac{\text{N}}{\text{m}^2} = 1\ \dfrac{\text{kg}}{\text{m}\cdot\text{s}^2}

where: Pa is the pascal (SI pressure unit), N is the newton (SI force unit), and the right-hand form shows pressure fully decomposed into base units.

Derivation ABuilding the derived unit for density from base units

Goal. Show that the "natural" SI unit of density, kg/m³, follows directly and unavoidably from the definitions of mass and length, with no extra assumptions.

Step 1. Start from the defining ratio. Density is defined operationally as mass per unit volume:

\rho = \frac{m}{V}

Here $m$ carries the SI base unit of mass (kg), and $V$ carries the unit of volume, itself derived from length.

Step 2. Express volume in base units. Volume is length cubed, since it measures the three-dimensional extent of a region of space:

V = \ell \times w \times h \quad \Rightarrow \quad [V] = \text{m} \times \text{m} \times \text{m} = \text{m}^3

No new base unit is invoked; volume is entirely a consequence of the meter.

Step 3. Substitute into the density ratio.

[\rho] = \frac{[m]}{[V]} = \frac{\text{kg}}{\text{m}^3}

This is the SI-coherent unit of density — it uses no numerical conversion factor, only the base units directly.

Step 4. Connect to the chemist's everyday unit. Chemists usually measure small samples in grams and cubic centimeters (or milliliters). Since $1\ \text{g} = 10^{-3}\ \text{kg}$ and $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$ :

1\ \dfrac{\text{g}}{\text{cm}^3} = \dfrac{10^{-3}\ \text{kg}}{10^{-6}\ \text{m}^3} = 1 \times 10^{3}\ \dfrac{\text{kg}}{\text{m}^3}

This confirms the two commonly used density units differ by exactly a factor of 1000 — g/cm³ values are always 1000 times smaller in magnitude than the equivalent kg/m³ value.

Step 5. Limiting-case sanity check. Consider a hypothetical substance with mass equal to its volume when both are measured in coherent SI units — that is, $m = V$ numerically with $m$ in kg and $V$ in m³. Then $\rho = 1$ kg/m³, matching the density of a very dilute gas (air is about 1.2 kg/m³ at room conditions), confirming the formula behaves sensibly at the low-density limit rather than producing some spurious extra factor.

Worked examples

Example 1 — Converting a density measurement between coherent SI units and everyday lab units A chemistry student weighs an irregular metal sample and finds its mass is 47.3 g. By water displacement, its volume is found to be 6.20 cm³. Report the density both in g/cm³ (lab convention) and in kg/m³ (coherent SI). Step 1. Compute density in lab units directly:

\rho = \frac{m}{V} = \frac{47.3\ \text{g}}{6.20\ \text{cm}^3} = 7.6290\ \text{g/cm}^3

Step 2. Round to three significant figures, matching the least precise input (47.3 g has 3 sig figs, 6.20 cm³ has 3 sig figs):

\rho \approx 7.63\ \text{g/cm}^3

Step 3. Convert to coherent SI (kg/m³) using the factor derived above, $1\ \text{g/cm}^3 = 1000\ \text{kg/m}^3$ :

\rho = 7.63\ \text{g/cm}^3 \times 1000\ \frac{\text{kg/m}^3}{\text{g/cm}^3} = 7.63 \times 10^{3}\ \text{kg/m}^3

This density (7.63 g/cm³) is close to that of steel (about 7.8 g/cm³) or zinc (7.14 g/cm³), so the number is physically reasonable — the sample is plausibly a metal alloy, not, say, aluminum (2.70 g/cm³) or gold (19.3 g/cm³).

Example 2 — Building a derived unit for molar concentration from base units, and checking it against a real solution A student dissolves 3.55 g of sodium chloride (NaCl, molar mass 58.44 g/mol) in enough water to make 250.0 mL of solution. Find the molar concentration in the SI-coherent unit (mol/m³) as well as the conventional chemistry unit (mol/L). Step 1. Convert mass to moles using molar mass:

n = \frac{3.55\ \text{g}}{58.44\ \text{g/mol}} = 0.060746\ \text{mol}

Step 2. Convert volume from milliliters to liters:

V = 250.0\ \text{mL} \times \frac{1\ \text{L}}{1000\ \text{mL}} = 0.2500\ \text{L}

Step 3. Compute molar concentration in the conventional unit, mol/L (often written M):

c = \frac{n}{V} = \frac{0.060746\ \text{mol}}{0.2500\ \text{L}} = 0.24298\ \text{mol/L} \approx 0.2430\ \text{mol/L}

Step 4. Convert to the fully coherent SI derived unit, mol/m³, using $1\ \text{L} = 10^{-3}\ \text{m}^3$ :

c = 0.2430\ \frac{\text{mol}}{\text{L}} \times \frac{1\ \text{L}}{10^{-3}\ \text{m}^3} = 243.0\ \text{mol/m}^3

This calculation, which is really a small application of the ideas developed further in Metric Prefixes and Unit Conversion, shows a general pattern: chemists routinely report values in convenient "chemistry-scale" units (mol/L, g/cm³) but every one of those units unpacks cleanly into the seven SI base units without ambiguity.

Limiting cases & common traps

Situation	What goes wrong	Correct approach
Reporting a bare number ("mass = 12")	No unit means no physical meaning	Always attach a unit to every reported quantity
Mixing g and kg, or mL and m³, mid-calculation	Off by a factor of 1000 (or 10⁶ for volume)	Convert everything to one consistent unit system before dividing/multiplying
Treating °C as if it were an SI base unit	Celsius is a derived, offset scale, not an SI base unit	Kelvin is the SI base unit; convert with $T(\text{K}) = T(^{\circ}\text{C}) + 273.15$
Assuming "liter" is an SI base unit	The liter is only an accepted non-SI unit tolerated alongside SI	The true coherent SI volume unit is m³; L is a convenient multiple
Ignoring significant figures when converting units	Reported answer implies false precision	Match sig figs to the least precise measured quantity, as in Example 1

The chemist behind it

The modern SI system did not arise from a single chemist's insight; it grew out of a centuries-long international effort, beginning with the French Academy of Sciences' decimal metric proposals in the 1790s, through the 1960 formal establishment of "Le Système International d'Unités," to the 2019 redefinition that anchored all seven base units to fixed values of fundamental physical constants rather than physical artifacts (such as the old platinum-iridium kilogram cylinder kept in France). That 2019 redefinition was a genuinely collaborative achievement of metrologists and physicists worldwide, but one figure whose earlier work made the whole constants-based approach conceivable deserves particular mention.

Origins · 1 minMax Planck and how this was discovered

Max Planck

1858–1947 · German theoretical physicist whose 1900 quantum hypothesis introduced the constant h that now defines the kilogram

Planck introduced his eponymous constant while explaining blackbody radiation, treating energy exchange as occurring in discrete quantized packets rather than continuously. He could not have anticipated that, more than a century later, metrologists would use the exact numerical value of the Planck constant to define the kilogram itself, replacing a physical metal cylinder with a universal, unchanging number tied to quantum mechanics. His work reshaped physics and, indirectly, the very foundation of how mass is measured in every chemistry laboratory today.

Ask the tutor: How do I systematically convert between any two SI-derived units without memorizing every conversion factor by heart?

Why does SI need exactly seven base units — why not more or fewer?

Seven was chosen because these seven quantities — length, mass, time, current, temperature, amount of substance, and luminous intensity — are the minimum, mutually independent set from which every other physical unit used in science can be constructed by multiplication and division. Historically the exact count has shifted slightly (candela was added later), but the modern consensus, ratified through international treaty, fixes the count at seven.

Is the liter really not an SI unit?

Correct — the liter (L) is not one of the seven base units, nor is it a strictly coherent SI derived unit. It is officially classified as a unit "accepted for use with SI" because $1\ \text{L} = 10^{-3}\ \text{m}^3$ exactly, making conversion trivial. Chemists use it constantly for convenience, but the truly coherent SI volume unit is the cubic meter.

Why did SI move away from physical objects like the platinum-iridium kilogram?

Physical artifacts can gain or lose mass over decades due to contamination, wear, or cleaning — the original kilogram cylinder actually drifted by tens of micrograms relative to its official copies over the 20th century. Defining the kilogram instead through a fixed numerical value of the Planck constant removes this drift entirely, because fundamental constants of nature do not change with time or location.

Do I need to memorize all seven SI base units for a first chemistry course?

You should recognize all seven, but in practice five dominate quantitative chemistry: the meter, kilogram, second, kelvin, and mole. The ampere appears mainly in electrochemistry, and the candela almost never appears in a typical general-chemistry course.

How does this connect to significant figures and unit conversions I'll do constantly?

Every unit conversion (grams to kilograms, milliliters to liters, Celsius to kelvin) is simply a multiplication by an exact conversion factor between two units built from the same or related base units. The topic of Metric Prefixes and Unit Conversion develops the systematic method (dimensional analysis) for doing this reliably, and it depends entirely on having the seven base units clearly fixed first.