SI Base Units

Every measurement in science rests on a foundation of agreed-upon reference quantities. The International System of Units — abbreviated SI from the French Système International d'Unités — provides exactly that foundation. Adopted in 1960 by the General Conference on Weights and Measures (CGPM) and most recently revised in 2019, SI defines seven base units from which every other unit of measurement can be derived. Whether you are measuring the speed of a rocket, the charge stored in a capacitor, or the brightness of a star, you are ultimately expressing your result in combinations of these seven units. The seven SI base quantities and their units are: length (metre, m), mass (kilogram, kg), time (second, s), electric current (ampere, A), thermodynamic temperature (kelvin, K), amount of substance (mole, mol), and luminous intensity (candela, cd). Each base unit is now defined by fixing the numerical value of a fundamental constant of nature — for example, the kilogram is defined by fixing Planck's constant $h = 6.626 \times 10^{-34}$ J s. This approach makes the definitions stable forever and independent of any physical artefact. Understanding SI base units is essential for dimensional analysis — a powerful technique for checking equations, converting between unit systems, and even deriving relationships between physical quantities. Every derived unit such as the newton (N), joule (J), or watt (W) can be expressed as a product of powers of the base units, e.g. $1\text{ N} = 1\text{ kg m s}^{-2}$ . Mastery of base units is therefore the first step toward fluency in all of physics.

Key takeaways

Metre (m) — Length
Kilogram (kg) — Mass
Second (s) — Time
Ampere (A) — Electric Current
Kelvin (K) — Thermodynamic Temperature
Mole (mol) — Amount of Substance
Candela (cd) — Luminous Intensity

Metre (m) — Length

The metre is the SI unit of length. Since 1983 it has been defined by fixing the speed of light in vacuum: $c = 299\,792\,458$ m s $^{-1}$ exactly. Therefore $1\text{ m}$ is the distance light travels in $1/299\,792\,458$ of a second. This makes the metre dependent on the second, which is defined first.

Kilogram (kg) — Mass

The kilogram is the SI unit of mass and the only base unit with a prefix in its name. Since the 2019 redefinition, it is defined by fixing Planck's constant: $h = 6.626\,070\,15 \times 10^{-34}$ kg m $^2$ s $^{-1}$ . Previously it was defined by a physical platinum-iridium cylinder kept near Paris — a unique and fragile artefact.

Second (s) — Time

The second is defined by fixing the caesium hyperfine transition frequency: $\Delta\nu_{\text{Cs}} = 9\,192\,631\,770$ Hz exactly. In other words, $1\text{ s}$ is the duration of $9\,192\,631\,770$ cycles of the microwave radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom. This definition makes atomic clocks the most accurate timekeepers ever built, with uncertainties below $10^{-16}$ .

Ampere (A) — Electric Current

The ampere is the SI unit of electric current. Since 2019, it is defined by fixing the elementary charge: $e = 1.602\,176\,634 \times 10^{-19}$ C, where $1\text{ C} = 1\text{ A s}$ . Therefore one ampere corresponds to approximately $6.242 \times 10^{18}$ elementary charges (electrons or protons) flowing past a cross-section per second.

Kelvin (K) — Thermodynamic Temperature

The kelvin is the SI unit of absolute temperature. It is defined by fixing the Boltzmann constant: $k_B = 1.380\,649 \times 10^{-23}$ J K $^{-1}$ . The kelvin scale starts at absolute zero, the lowest possible temperature, where a classical ideal gas would have zero volume and zero pressure. The freezing point of water is $273.15$ K.

Mole (mol) — Amount of Substance

The mole is defined by fixing the Avogadro constant: $N_A = 6.022\,140\,76 \times 10^{23}$ mol $^{-1}$ . One mole of any substance contains exactly $6.022\,140\,76 \times 10^{23}$ elementary entities (atoms, molecules, ions, etc.). This links macroscopic quantities to atomic-scale counting.

Candela (cd) — Luminous Intensity

The candela is the SI unit of luminous intensity — the power emitted by a light source in a particular direction, weighted by the sensitivity of the human eye. It is defined by fixing the luminous efficacy of monochromatic radiation of frequency $540 \times 10^{12}$ Hz (green light): $K_{cd} = 683$ lm W $^{-1}$ . Unlike the other base units, the candela is inherently biological, tied to human visual perception.

The Key Equation

$$[Q] = \text{m}^{\alpha}\,\text{kg}^{\beta}\,\text{s}^{\gamma}\,\text{A}^{\delta}\,\text{K}^{\epsilon}\,\text{mol}^{\zeta}\,\text{cd}^{\eta}

- **\alpha** — length exponent (dimensionless): Power to which the metre appears in the dimensional formula - **\beta** — mass exponent (dimensionless): Power to which the kilogram appears - **\gamma** — time exponent (dimensionless): Power to which the second appears; negative for quantities like frequency - **\delta** — current exponent (dimensionless): Power to which the ampere appears; e.g. 1 for charge (C = A s) - **\epsilon,\zeta,\eta** — temperature, amount, luminosity exponents (dimensionless): Powers for kelvin, mole, and candela respectively ## Worked Example **Problem.** Express the SI unit of pressure (the pascal, Pa) entirely in terms of SI base units, and state its dimensional formula.

1\text{ Pa} = 1\text{ kg m}^{-1}\text{s}^{-2}

**Answer.** 1 Pa = 1 kg m⁻¹ s⁻²

Figure

Diagram

Origins · 1 minGiovanni Giorgi and how this was discovered

Giovanni Giorgi

1871–1950 · Italian

Giorgi proposed in 1901 that a coherent system of units based on the metre, kilogram, and second (MKS), supplemented by one electrical unit, would resolve the inconsistencies between the CGS electromagnetic and electrostatic unit systems. His proposal, presented to the International Electrotechnical Commission, became the foundation of the modern SI system adopted in 1960. Giorgi was an electrical engineer by training and was primarily motivated by practical problems in electrical power engineering — he wanted engineers worldwide to stop fighting over whether to use CGS-esu or CGS-emu units for the same calculation.

Dimensional Analysis — Dimensional analysis uses the SI base unit dimensions to check equations and derive relationships between physical quantities.
SI Derived Units — All derived units such as the newton, joule, and watt are formed from products and powers of the seven SI base units.
SI Prefixes and Scientific Notation — SI prefixes (kilo-, milli-, nano-, etc.) are applied to base units to express very large or very small measurements conveniently.
Measurement Uncertainty and Significant Figures — Understanding base units is prerequisite to properly reporting measurements with correct units and appropriate uncertainty.
Unit Conversion — Converting between unit systems (e.g. CGS to SI) requires knowing the base units and their relationships to non-SI units.