The SI Base Units: The Seven Defining Quantities of Modern Measurement

Pair this deep dive with our overview of the International System of Units and calculators such as the length conversion tools and the average speed calculator to see how constant-based definitions translate into practical problem-solving.

Introduction

The International System of Units (SI) is the global language of measurement. At its foundation are seven base quantities—time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity—each associated with a base unit and a definition anchored to fundamental physical constants. Since the 2019 SI revision, these units are defined by exact numerical values of carefully chosen constants, ensuring long-term stability, universality, and technical robustness.

This article explains the logic and structure of the SI, the 2019 redefinition, and each of the seven base units. It emphasizes correct symbols, conceptual clarity, historical context, practical realization, and the role of base units in scientific and industrial practice.

The Architecture of the SI

Coherence and Derived Units

The SI is coherent: when you express laws of physics using SI units, equations keep their form without hidden conversion factors. From the seven base units—second (s), metre (m), kilogram (kg), ampere (A), kelvin (K), mole (mol), candela (cd)—you build derived units such as the newton (N = kg·m·s⁻²), pascal (Pa = N·m⁻²), joule (J = N·m), watt (W = J·s⁻¹), coulomb (C = A·s), volt (V = W·A⁻¹), ohm (Ω = V·A⁻¹), and many others. Dimensionless derived quantities (e.g., radian, steradian) coexist consistently within the SI framework.

The 2019 Redefinition: Constants as Anchors

Historically, some SI units referenced artifacts or material properties (notably, the kilogram’s platinum-iridium prototype). In 2019, the SI was redefined to fix exact numerical values for seven constants:

  • ΔνCs (the unperturbed ground-state hyperfine transition frequency of the cesium-133 atom)
  • c (speed of light in vacuum)
  • h (Planck constant)
  • e (elementary charge)
  • kB (Boltzmann constant)
  • NA (Avogadro constant)
  • Kcd (luminous efficacy of monochromatic radiation of frequency 540 THz)

Each base unit is now defined in terms of one or more of these constants, which are invariant and universally accessible through experiment. This shift replaces vulnerable references (artifacts, material properties) with physics itself.

The Seven Base Quantities and Their Units

Time — the second (s)

Definition. The second is defined by fixing the numerical value of the cesium-133 hyperfine transition frequency to ΔνCs = 9 192 631 770 s⁻¹ (exact). One second is the duration of 9 192 631 770 periods of the radiation corresponding to this transition.

History and rationale. Early timekeeping used astronomical days and years; in 1967 the SI adopted the atomic definition to achieve stability and reproducibility independent of Earth’s rotation. Atomic clocks provide extraordinary precision and underpin global navigation and timing.

Realization. Primary frequency standards (cesium fountain clocks) and advanced optical clocks (based on ions or neutral atoms) realize the second with fractional uncertainties below 10⁻¹⁶–10⁻¹⁸. Time is disseminated via GNSS, Two-Way Satellite Time and Frequency Transfer, and optical fiber links.

Applications. Telecommunications, synchronization of power grids, finance time-stamping, deep-space navigation, tests of fundamental physics, and any measurement requiring precise timing or frequency.

Length — the metre (m)

Definition. The metre is defined by fixing the numerical value of the speed of light in vacuum to c = 299 792 458 m·s⁻¹ (exact). One metre is the distance light travels in 1/299 792 458 of a second.

History and rationale. The metre evolved from Earth-based definitions to the krypton-86 orange line (1960), and since 1983 has been defined via c, linking length to atomic time. Laser interferometry and frequency combs provide practical realization across scales.

Realization. Stabilized lasers with traceable frequencies, optical frequency combs, and interferometric setups calibrate gauge blocks, coordinate measuring machines, and geodetic baselines.

Applications. Precision manufacturing, geodesy and surveying, semiconductor lithography, satellite ranging, and experimental physics requiring nanometre to kilometre accuracy.

Mass — the kilogram (kg)

Definition. The kilogram is defined by fixing the numerical value of the Planck constant to h = 6.626 070 15 × 10⁻³⁴ J·s (exact), with 1 J = 1 kg·m²·s⁻² and the metre and second defined as above. Mass is thus anchored to quantum physics rather than a physical artifact.

History and rationale. For over a century, the kilogram relied on a platinum-iridium prototype; small drifts between the artifact and its copies motivated a physics-based definition.

Realization.

  • Kibble balance: equates mechanical power (mgv) with electrical power via quantum electrical standards (Josephson and quantum Hall effects), linking kg to h, e, and frequency.
  • X-ray crystal density (XRCD) / Avogadro route: counts atoms in nearly perfect silicon spheres to connect mass to NA.

Applications. High-precision mass metrology for pharmaceuticals and precious metals, process industries, and as a cornerstone for derived mechanical units (newton, pascal, joule).

Electric current — the ampere (A)

Definition. The ampere is defined by fixing the numerical value of the elementary charge to e = 1.602 176 634 × 10⁻¹⁹ C (exact), with 1 C = 1 A·s. One ampere corresponds to the flow of 1/e elementary charges per second.

History and rationale. The previous definition used the magnetic force between ideal conductors. Fixing e brings current directly to the quantum scale and unifies electrical units through the Josephson and quantum Hall effects.

Realization.

  • Single-electron pumps generate quantized currents I = n e f.
  • Quantum voltage and resistance standards (Josephson arrays, quantum Hall devices) establish V and Ω; in combination with time, they realize A.

Applications. Electrical calibration (V, Ω, A), power and energy metering, quantum electronics, precision sensor development, and all electrical and electronic engineering.

Thermodynamic temperature — the kelvin (K)

Definition. The kelvin is defined by fixing the numerical value of the Boltzmann constant to kB = 1.380 649 × 10⁻²³ J·K⁻¹ (exact). Temperature is thereby related to average thermal energy per microscopic degree of freedom.

History and rationale. Formerly tied to the triple point of water, the kelvin now rests on a universal constant, making it independent of material properties while preserving the practical water triple-point as a reference.

Realization. Primary thermometry techniques—acoustic gas thermometry, Johnson-noise thermometry, dielectric constant gas thermometry—link temperature to fundamental physics. Interpolating instruments (platinum resistance thermometers, thermocouples) provide practical scales across ranges.

Applications. Climate and atmospheric science, materials processing, cryogenics and superconductivity, medical thermometry, and any process control requiring traceable temperature.

Amount of substance — the mole (mol)

Definition. The mole is defined by fixing the numerical value of the Avogadro constant to NA = 6.022 140 76 × 10²³ mol⁻¹ (exact). One mole contains exactly 6.022 140 76 × 10²³ specified entities (atoms, molecules, ions, electrons, …), chosen with the entity specified explicitly.

History and rationale. The mole historically connected macroscopic chemistry to atomic counts via molar masses. Fixing NA decouples the mole from the kilogram while maintaining the familiar molar-mass scale (in practice, values remain consistent for routine chemistry).

Realization. Counting methods (e.g., XRCD silicon spheres), coulometry, gravimetry, and isotope-dilution mass spectrometry underpin high-accuracy chemical metrology.

Applications. Stoichiometry, reaction engineering, environmental monitoring, clinical chemistry, and all analyses where quantifying entities is essential.

Luminous intensity — the candela (cd)

Definition. The candela is defined by fixing the numerical value of the luminous efficacy of monochromatic radiation of frequency 540 THz (green light) to Kcd = 683 lm·W⁻¹ (exact). A source emitting monochromatic radiation at 540 THz with radiant intensity 1/683 W·sr⁻¹ has luminous intensity 1 cd in that direction.

History and rationale. Earlier human-based visual standards (e.g., “standard candle”) were replaced by a photometric definition tied to radiometric power weighted by the human photopic response. The 1979 definition (retained in 2019) ensures consistent lighting metrology worldwide.

Realization. Photometers calibrated to the CIE photopic luminous efficiency function, absolute radiometric standards, and spectroradiometers realize the candela and related photometric units (lumen, lux).

Applications. Lighting design and regulation, display calibration, imaging and remote sensing, and safety signaling—anywhere human visual effectiveness matters.

Correct Symbols, Formatting, and Good Practice

  • Typography: Quantity symbols italic (e.g., m for mass), unit symbols upright (kg, m, s, A, K, mol, cd). Unit symbols are not pluralized: write “5 kg,” not “5 kgs.”
  • Spacing: Insert a space between the number and unit (e.g., 20 °C, 1.5 m).
  • Prefixes: SI prefixes apply to unit symbols (e.g., mm, µs, kA). Avoid double prefixes; note that kilogram uniquely contains a prefix in its name—use mg, g, kg, not “µkg.”
  • Single solidus: Prefer exponents or a single solidus in compound units: J·kg⁻¹·K⁻¹ rather than “J/kg/K.”
  • Angles: Use radian (rad) and steradian (sr) for clarity in frequency/phase contexts (e.g., rad·s⁻¹ vs s⁻¹).

Why Constants-Based Definitions Matter

  1. Universality. Any laboratory can, in principle, realize the units by accessing the same constants with suitable apparatus, removing dependence on unique artifacts.
  2. Stability. Physical constants do not drift; measurement technology can improve indefinitely without redefining units.
  3. Interoperability. Quantum electrical standards unify voltage, resistance, and current; thermodynamic temperature ties directly to statistical physics; counting links chemistry to exact integer quantities.
  4. Innovation-ready. New technologies (optical clocks, atom interferometers, quantum sensors) can realize SI units with higher accuracy without changing the definitions.

Examples: From Base to Derived Units

  • Force: F = m a ⇒ N = kg·m·s−2.
  • Pressure: p = F/A ⇒ Pa = N·m−2.
  • Energy: E = F s ⇒ J = N·m.
  • Power: P = E/t ⇒ W = J·s−1.
  • Charge: Q = I t ⇒ C = A·s.
  • Electric potential: V = W/Q ⇒ V = W·A−1. These follow directly from the base units, illustrating coherence and dimensional consistency.

Common Pitfalls (and How to Avoid Them)

  • Mis-casing unit symbols: K (kelvin), not “°K”; A (ampere), not “amp”; mol, not “mole.”
  • Confusing frequency and angular frequency: Hz = s⁻¹ for cycles per second; rad·s⁻¹ for angular frequency ω.
  • Pluralizing unit symbols: never add “s” to symbols (write 5 cm, not “5 cms”).
  • Missing conditions: many measurements depend on temperature, pressure, wavelength, or bandwidth. State them.
  • Mixing decimals and separators: group long numbers with thin spaces (e.g., 12 345 678) and use a consistent decimal marker.

The Enduring Importance of the Seven

The SI base units are more than labels: they are interfaces between physical theory, instrumentation, and real-world decisions. The second and metre anchor navigation and communications; the kilogram underpins trade and manufacturing; the ampere secures energy markets and electronics; the kelvin stabilizes climate records and process control; the mole guarantees chemical traceability; the candela standardizes lighting and imaging. By fixing definitions to natural constants, the SI assures that as technology advances, the meaning of a unit never changes—only our ability to realize it improves.

Conclusion

The seven SI base quantities—time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity—form a coherent structure for quantifying the world. The 2019 constant-based definitions give each base unit a precise, immutable anchor in physics, enabling tighter uncertainties, seamless global comparability, and resilience against obsolescence. For scientists, engineers, regulators, and data curators, mastering these definitions and their correct usage is foundational. It ensures that equations balance, instruments agree, and knowledge accumulates on a stable quantitative bedrock—exactly what a world of interoperable science and technology requires.

Continue applying these ideas through our unit converters, revisit the guide to units of measurement, and explore calculators such as the boiling point at altitude calculator for real-world practice grounded in SI coherence.