Fundamental Physical Constants: Reference and Significance
Fundamental physical constants are fixed numerical values that appear throughout the equations of physics and define the quantitative relationships governing the natural world. This page covers the principal constants, their formal definitions under the International System of Units (SI), the mechanisms by which they are determined and maintained, and the contexts in which precise constant values become operationally critical. The physics constants reference and associated physics formulas and equations depend entirely on these foundational values for dimensional consistency and predictive accuracy.
Definition and scope
A fundamental physical constant is a quantity whose value is not derivable from first principles within the current framework of physics and must therefore be measured empirically and fixed by international agreement. The Committee on Data for Science and Technology (CODATA), a standing committee of the International Science Council, coordinates the global least-squares adjustment of recommended constant values. The 2018 CODATA adjustment, published in the journal Reviews of Modern Physics and adopted by the International Bureau of Weights and Measures (BIPM), redefined the SI base units such that seven constants were assigned exact fixed values rather than measured approximations (BIPM SI Brochure, 9th edition).
The seven defining constants of the 2019 SI revision are:
- Hyperfine transition frequency of caesium-133 (ΔνCs): exactly 9,192,631,770 Hz — defines the second
- Speed of light in vacuum (c): exactly 299,792,458 m/s — defines the metre
- Planck constant (h): exactly 6.62607015 × 10⁻³⁴ J·s — defines the kilogram
- Elementary charge (e): exactly 1.602176634 × 10⁻¹⁹ C — defines the ampere
- Boltzmann constant (k): exactly 1.380649 × 10⁻²³ J/K — defines the kelvin
- Avogadro constant (Nₐ): exactly 6.02214076 × 10²³ mol⁻¹ — defines the mole
- Luminous efficacy of monochromatic radiation at 540 × 10¹² Hz (Kcd): exactly 683 lm/W — defines the candela
Beyond these defining constants, physics relies on derived constants — such as the fine-structure constant (α ≈ 1/137.036), the gravitational constant (G ≈ 6.674 × 10⁻¹¹ N·m²/kg²), and the proton mass (mₚ ≈ 1.67262192 × 10⁻²⁷ kg) — whose values are determined by measurement and carry associated uncertainties. The physics measurement and units framework provides the dimensional structure within which these constants operate. Understanding how the entire scientific method incorporates such fixed values is addressed in the how science works conceptual overview.
How it works
Constants enter physics through theoretical structures: the speed of light c appears in Maxwell's equations (see electromagnetism fundamentals) and in Einstein's mass-energy relation E = mc² (see special and general relativity); Planck's constant h is the foundational quantity of quantum mechanics, setting the minimum unit of action; the gravitational constant G anchors every calculation in gravity and gravitational fields and scales up through astrophysics and cosmology.
Measurement of non-fixed constants relies on multiple independent experimental methods whose results are weighted and reconciled in CODATA adjustments. The gravitational constant G, for example, is measured via torsion balance experiments, pendulum methods, and atomic interferometry. As of the 2018 CODATA adjustment (NIST CODATA Values), G carries a relative standard uncertainty of approximately 2.2 × 10⁻⁵ — the largest fractional uncertainty among the major constants, reflecting the comparative weakness and non-shielding nature of gravity.
Exact vs. measured constants — a key contrast:
| Category | Example | Uncertainty |
|---|---|---|
| SI-defining (exact by convention) | Speed of light c | Zero (by definition) |
| Measured (empirically adjusted) | Gravitational constant G | ~2.2 × 10⁻⁵ relative |
| Dimensionless (measured) | Fine-structure constant α | ~1.5 × 10⁻¹⁰ relative |
The fine-structure constant α is dimensionless — its value is independent of the unit system used — making it a particularly deep quantity. Its proximity to 1/137 has no derivation within the Standard Model (particle physics and Standard Model) and remains an open theoretical question.
Common scenarios
Fundamental constants appear as non-negotiable inputs across the full spectrum of physics subdisciplines:
- Atomic and nuclear physics: The Bohr radius (a₀ ≈ 5.292 × 10⁻¹¹ m), derived from e, mₑ, h, and ε₀, sets the characteristic scale of electron orbitals (see atomic structure and models). Radioactive decay calculations in radioactivity and decay use the nuclear binding energies expressed through c².
- Thermodynamics: The Boltzmann constant k directly links macroscopic temperature to microscopic kinetic energy. All equations of statistical mechanics and thermodynamics use k or the gas constant R = Nₐ × k = 8.314462618 J/(mol·K) (NIST).
- Semiconductor and condensed matter physics: The electron charge e and Planck constant h determine quantized conductance and the behavior of charge carriers in semiconductor physics and solid-state and condensed matter physics.
- Precision timekeeping and GPS: The caesium-133 hyperfine frequency that defines the second is directly implemented in atomic clocks. GPS satellite systems require relativistic corrections involving both c and G to maintain positional accuracy.
- Cosmology: The ratio of the gravitational constant to the Hubble constant determines critical density in cosmological models. Anomalies in expected values feed into active research on dark matter and dark energy.
Decision boundaries
When working with physical constants, the choice between using an exact SI-defining value and a CODATA-measured value is determined by the physical context:
Use the exact SI value when the calculation involves a quantity that is defined in terms of the 2019 SI base units — e.g., converting energy in joules using Planck's constant or computing charge quantities using the elementary charge. No uncertainty propagation is needed for these inputs.
Use CODATA recommended values with stated uncertainty when the constant is empirically measured (e.g., G, α, mₚ) and the precision of the result affects experimental design, instrument calibration, or theoretical comparison. Uncertainty must be propagated through the calculation per standard metrology protocols (JCGM 100:2008, the GUM — BIPM).
Unit-system choice matters when constants take different numerical forms. In Gaussian CGU units, the speed of light appears explicitly in electromagnetic force equations; in SI, it is absorbed into the permittivity and permeability of free space. Researchers in quantum field theory frequently employ natural units where ħ = c = 1, eliminating explicit constant factors from equations — but reintroducing them when converting to measurable quantities.
The physicsauthority.com index catalogs the full scope of physics topics across which these constants are applied, from fluid mechanics and dynamics to plasma physics to medical physics applications. Constants like c, h, and e are not domain-specific — they are cross-cutting values whose precision sets the ceiling on measurement accuracy in every subdiscipline represented in applied physics and real-world applications and physics in engineering.
References
- BIPM — International Bureau of Weights and Measures: SI Brochure, 9th Edition
- NIST — CODATA Internationally Recommended 2018 Values of the Fundamental Physical Constants
- CODATA — Committee on Data for Science and Technology (International Science Council)
- BIPM — JCGM 100:2008 Evaluation of Measurement Data (GUM)
- NIST Physical Measurement Laboratory — Fundamental Constants