Fundamental Constants Used in Gravity

These are the constants used when a gravity calculation must be restored from the site’s natural-unit convention to SI. The table separates four logically different statuses: an exact SI defining value, an exact quantity derived from one, a measured constant with uncertainty, and an exact nominal conversion. Their physical roles and dimensional use are developed in Physical Foundations. Values and source editions were checked on 2026-08-23.

SI constants and the measured gravitational coupling

The 2026 SI Brochure fixes $c$, $h$, $e$, and $k_{\mathrm B}$ exactly; these numbers define units and therefore do not carry experimental uncertainty (BIPM 2026, § 2.2 and Table 1, printed pp. 123–124, PDF). The reduced Planck constant is also exact because $\hbar\equiv h/(2\pi)$, although its decimal expansion does not terminate. The 2022 CODATA adjustment reproduces those values and gives the measured value of $G$ (NIST CODATA 2022, NIST SP 961 single-page wall chart, p. 1, PDF).

Quantity	Accepted SI value	Status
Speed of light, $c$	$299\,792\,458\ \mathrm{m\,s^{-1}}$	SI-defining, exact
Planck constant, $h$	$6.626\,070\,15\times10^{-34}\ \mathrm{J\,s}$	SI-defining, exact
Reduced Planck constant, $\hbar$	$1.054\,571\,817\ldots\times10^{-34}\ \mathrm{J\,s}$	Derived exact: $h/(2\pi)$
Elementary charge, $e$	$1.602\,176\,634\times10^{-19}\ \mathrm C$	SI-defining, exact
Boltzmann constant, $k_{\mathrm B}$	$1.380\,649\times10^{-23}\ \mathrm{J\,K^{-1}}$	SI-defining, exact
Newtonian gravitational constant, $G$	$6.674\,30(15)\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}}$	Measured; one-standard-deviation uncertainty

For a measured value, digits in parentheses give the standard uncertainty in the final quoted digits. Thus

$$\begin{aligned} G&=6.67430\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}},\\ u(G)&=0.00015\times10^{-11}\ \mathrm{m^3\,kg^{-1}\,s^{-2}}. \end{aligned}$$

with relative standard uncertainty $u(G)/G\simeq2.2\times10^{-5}$, about $22$ parts per million. Writing an uncertainty after $c$, $h$, $e$, or $k_{\mathrm B}$ would be a category error: experimental measurements test the realization of their units, not the exact defining values themselves. Likewise, the ellipsis in the displayed decimal for $\hbar$ does not make $\hbar$ measured or uncertain; the exact statement is $h/(2\pi)$.

Nominal solar conversion factors

The IAU defines nominal solar quantities as exact conversion factors, marked with a superscript $\mathrm N$. They are not measurements of the evolving physical Sun (IAU 2015 Resolution B3, Recommendations 1–4 and solar table, printed pp. 1–2, PDF).

Nominal quantity	Exact conversion value
Solar radius, $\mathcal R_\odot^{\mathrm N}$	$6.957\times10^8\ \mathrm m$
Solar mass parameter, $(GM)_\odot^{\mathrm N}$	$1.327\,124\,4\times10^{20}\ \mathrm{m^3\,s^{-2}}$

Orbital dynamics normally determines a gravitational parameter $\mu=GM$ more directly than it determines a mass in kilograms. Using $(GM)_\odot^{\mathrm N}$ therefore avoids injecting the comparatively large uncertainty of $G$ into a calculation whose equations require only $GM$. If a kilogram conversion is genuinely needed, it must be written as

$$M_{\odot,\mathrm{conv}} =\frac{(GM)_\odot^{\mathrm N}}{G}.$$

That quotient is not an exact nominal solar mass: it inherits the chosen measured value and uncertainty of $G$. Keeping $(GM)_\odot^{\mathrm N}$ intact also prevents a later multiplication by $G$ from falsely treating two correlated uses of the same measured constant as independent information.

When values must be rechecked

Use the exact defining or nominal value when performing a unit conversion. Use the measured $G$ value, uncertainty, and named CODATA adjustment when a result really depends on kilograms. A superseding BIPM edition, CODATA adjustment, or IAU resolution requires the values and their source precision to be rechecked; no decimal should be silently updated from a secondary table.

References

• Bureau International des Poids et Mesures. The International System of Units (SI). 9th ed., version 4.01 (2026), § 2.2 and Table 1, printed pp. 123–124. DOI. Official PDF.
• International Astronomical Union. “Resolution B3 on Recommended Nominal Conversion Constants for Selected Solar and Planetary Properties.” XXIX General Assembly (2015), Recommendations 1–4 and solar conversion table, printed pp. 1–2. Official PDF.
• Mohr, Peter J., David B. Newell, Barry N. Taylor, and Eite Tiesinga. “CODATA Recommended Values of the Fundamental Physical Constants: 2022.” Reviews of Modern Physics 97 (2025): 025002. DOI. National Institute of Standards and Technology, CODATA Recommended Values: 2022, NIST SP 961 (May 2024), one-page table. Official wall chart.