Fundamental Physical Constants: Reference and Significance
The universe runs on a fixed set of numbers. Fundamental physical constants — quantities like the speed of light, Planck's constant, and the elementary charge — appear in the equations governing everything from atomic structure to the expansion of space. This page covers what those constants are, why they hold the values they do (or why that question remains open), and how physicists use them in practice. It also draws the important line between constants that are defined by agreement and those that are measured against nature.
Definition and scope
A fundamental physical constant is a physical quantity whose value cannot be derived from more basic principles within current theory and must be determined through experiment. The NIST Reference on Constants, Units, and Uncertainty maintains the internationally recognized set of values, updated periodically through the CODATA (Committee on Data for Science and Technology) adjustment process.
The scope of "fundamental" is itself a precision target. Physicists distinguish three categories:
- Dimensionless constants — pure numbers, independent of any unit system. The fine-structure constant α ≈ 1/137.036 is the clearest example. Because it carries no units, its value is the same for any civilization using any measurement system.
- Dimensional constants with fixed definitions — since the 2019 revision of the International System of Units (SI), seven constants were assigned exact values by definition (BIPM SI Brochure, 9th edition). The speed of light c is now exactly 299,792,458 metres per second, and Planck's constant h is exactly 6.62607015 × 10⁻³⁴ joule-seconds. These are no longer measured — they define the metre, the kilogram, and other base units.
- Dimensional constants that remain measured — the gravitational constant G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² carries the largest relative uncertainty of any major constant, roughly 22 parts per million (CODATA 2018 recommended values, NIST).
How it works
Constants enter physics through the equations that describe interactions. The speed of light c links energy and mass in Einstein's E = mc²; Planck's constant h sets the quantum of action in E = hf, connecting a photon's energy to its frequency; Boltzmann's constant k_B = 1.380649 × 10⁻²³ joules per kelvin bridges the microscopic world of particle kinetics to the macroscopic concept of temperature.
What makes the 2019 SI revision consequential is the inversion of the measurement relationship. Before 2019, the kilogram was defined by a platinum-iridium cylinder kept in a vault outside Paris. Planck's constant was measured against that artifact. After 2019, Planck's constant is fixed, and the kilogram is derived from it via the Kibble balance — a device that equates mechanical and electromagnetic power. The artifact in Paris became scientifically redundant overnight. For a broader look at how measurement frameworks underpin scientific method, the conceptual overview of how science works provides useful context.
Common scenarios
Constants appear so routinely that their role becomes invisible until something depends critically on their precision.
- GPS timing: Relativistic corrections to satellite clocks rely on both c and G. An error of 1 part in 10⁸ in c would accumulate to roughly 3 metres of positional error per day.
- Semiconductor fabrication: The Bohr radius, a₀ = 5.29177 × 10⁻¹¹ metres, sets the scale for atomic electron orbitals. Engineers designing transistors at the 3-nanometre node are working at roughly 57 Bohr radii — close enough that quantum tunnelling becomes a design constraint, not a theoretical curiosity.
- Cosmology: The ratio of the gravitational constant to the Hubble constant determines whether the observable universe is flat, open, or closed. Even small shifts in G at cosmological scales propagate into estimates of dark matter density.
- Pharmaceutical metrology: Drug concentration standards traced to the SI rely on Avogadro's number, N_A = 6.02214076 × 10²³ mol⁻¹, now also defined exactly as of 2019.
The key dimensions and scopes of physics page maps how these constants distribute across different branches of the discipline — from quantum mechanics to thermodynamics to general relativity.
Decision boundaries
The critical distinction in working with constants is defined versus measured, and the consequences run in opposite directions.
A defined constant carries zero uncertainty by construction. Using c = 299,792,458 m s⁻¹ in a calculation introduces no measurement error from that term — only from whatever other quantities appear alongside it. This is why the 2019 SI revision improved reproducibility of mass standards worldwide without any new experimental discovery; it was an accounting decision with real metrological consequences.
A measured constant like G carries genuine uncertainty that propagates through any result. The gravitational constant has resisted precision improvement partly because gravity is so weak relative to electromagnetic forces that even tiny vibrations in laboratory floors contaminate measurements. Current experiments, including torsion balance and atom interferometry methods, have not yet closed the gap between competing published values — a tension the physics community has not fully resolved as of the CODATA 2018 dataset.
A second boundary concerns dimensionless versus dimensional constants. Whether c or h is "really" constant cannot be answered by measuring them in SI units, because those units are now defined through those constants. Only dimensionless combinations — like α — can be tested for constancy across cosmic time without circular logic. Astronomical spectroscopy of quasar absorption lines has constrained variation in α to below 10⁻⁵ over roughly 10 billion years (Webb et al., published in Physical Review Letters), making it one of the most stringent tests of whether the laws of physics are themselves stable.