The gravitational constant, G, is the number that sets the strength of the pull in Newton's law, F = Gm₁m₂/r². Its recommended value is 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², with a standard uncertainty of 22 parts per million (ppm). It has stood since the 2018 adjustment, because no new data entered the fit after 2018. We reran the fit on the sixteen experiments behind it and reproduced CODATA's result. They span 551 ppm. In 41 of the 120 possible pairs, two results sit more than three combined standard uncertainties apart. The set is consistent with a single value only once every error bar is multiplied by 3.9, a factor CODATA chose itself.
Scatter among the sixteen enters the recommended value
NIST's G value page carries the current figure; the ppm column is our arithmetic on its listings.
| Adjustment | G (10⁻¹¹ m³ kg⁻¹ s⁻²) | Relative uncertainty (ppm) |
|---|---|---|
| 2010 | 6.67384 | 120 |
| 2014 | 6.67408 | 46 |
| 2018 | 6.67430 | 22 |
| 2022 | 6.67430 | 22 |
Five of the sixteen inputs quote their own uncertainty below 22 ppm, the best two about 12, so the combined value is about twice as uncertain as the best single experiment. Averaging usually works the other way.
The two smallest uncertainties among the sixteen come from Huazhong University of Science and Technology in Wuhan, working with Sun Yat-sen University. Li and colleagues reported in Nature in 2018 two values with relative uncertainties of 11.64 and 11.61 ppm, "the smallest uncertainties reported until now". The two differ by 45 ppm, or 2.7 combined standard uncertainties. The full range runs from 6.67191 (LENS-14) to 6.67559 (BIPM-01), in line with the abstract's "discrepancy of up to 0.05 per cent".
A factor of 3.9 feeds that scatter into every error bar
The CODATA 2022 report says there were "no changes in or additions to these data" after the 2018 closing date, and that the same expansion factor was kept. We recomputed the weighted fit from its table of inputs and their stated correlations. With the uncertainties as published, χ² is 195.7 on 15 degrees of freedom, a Birge ratio of 3.6. Multiplied by 3.9, χ² falls to 12.87 (CODATA gives 12.9) and the Birge ratio to 0.93.
The factor changes the error bar and leaves the value alone: the mean is 6.674300 either way. CODATA's wording is that it "reduces all normalized residuals to 2 or less". The experiments still disagree pair by pair: the largest gap is BIPM-14 against JILA-18, at 9.9 combined standard uncertainties. That is measured against each laboratory's own stated uncertainty and shows no laboratory to be wrong.
Uncertainty in G lands on kilograms and bypasses orbits
Orbits and spacecraft tracking measure the product GM, and far more tightly. The IERS Conventions, Table 1.1, give Earth's GM as 3.986004418 × 10¹⁴ m³ s⁻² ± 8 × 10⁵ (the TCG-compatible value). That is a relative uncertainty of 2.0 × 10⁻⁹, about 11,200 times better than G's. For the Sun the ratio is about 300,000.
The IAU's 2015 Resolution B3 calls G "one of the least precisely determined constants" and asks that a mass needed in kilograms be written as GM/G, with the G used stated. Dividing the IERS figure by CODATA's G, Earth's mass is 5.97217 × 10²⁴ kg ± 1.3 × 10²⁰ kg.
At a fixed period, an orbit's radius goes as the cube root of GM. GM's uncertainty therefore moves a satellite's radius by about 0.7 parts per billion. If Earth's mass were held fixed and G moved by its standard uncertainty instead, the radius would move by 7.5 ppm, about 11,200 times more. Both figures are ours.
Rounded masses inject a larger error into GM
The usual way to lose accuracy is rebuilding GM from two rounded numbers. With 6.6743 × 10⁻¹¹ and Earth's mass as 5.972 × 10²⁴ kg, GM comes out 28 ppm low on our arithmetic. With 6.67 and 5.97, it is 1,007 ppm low, about 45 times G's own uncertainty.
Singapore's SEAB H2 Physics 9749 syllabus data list gives "G = 6.67 × 10–11 N m2 kg–2", as does 9478, examined from 2026. That is the value examinees are expected to use. We tested what that value does to a three-figure answer, over 2,146,689 combinations of masses and distance with leading digits spread evenly from 1.00 to 9.96, which exam numbers are not. Against 6.6743, the answer with 6.67 changed in 25.4% of them. Rounding to 6.674 changed 1.8%, the same share as moving G across its ±1 standard uncertainty band.
Until 3 November 2026 the worked Earth and Moon example in our Newton's gravitational force calculator printed 1.98 × 10²⁰ N beside G = 6.674, which gives 1.99. The revision of that date adds a Value of G menu. Its Earth and Moon preset (5.97 × 10²⁴ kg, 7.35 × 10²² kg, 3.84 × 10⁸ m) gives 1.99 × 10²⁰ N with CODATA's value and 1.98 × 10²⁰ N with the exam data list's.
Cavendish's density passes to G only through later arithmetic
Henry Cavendish's paper, read to the Royal Society on 21 June 1798, is titled "Experiments to determine the Density of the Earth". The method, and the apparatus, came from "the late Rev. John Michell". Searching the text, we found no "constant of gravitation". His answer is a density: 5.48 times that of water. A 2025 study of textbooks by Persson traces the claim that Cavendish determined G to C. V. Boys in 1889, and names Cornu and Baille in 1873 as the earliest derivation the author found.
His table on page 520 lists 29 densities. He gave the first wire's mean as 5.48 and wrote that the latter wire's "comes out the same". On the printed table, the six first-wire rows average 5.31, and the latter 23 average 5.483. All 29 together give 5.448, a figure often quoted, which he did not print.
Is one first-wire row, 4.88, a misprint for 5.88? We checked the row's own readings. Density times arm movement, divided by the square of the vibration time, comes out between 0.3317 and 0.3323 for all six rows, and the other five predict 4.883 for the third. The printed 4.88 fits, which places the slip in the mean. We could not find this row check published, though we searched only lightly.
Converting his density to G is our arithmetic, with g = 9.80665 m s⁻² and a 6,371 km radius: 5.448 gives 6.745 × 10⁻¹¹, and 5.48 gives 6.706 × 10⁻¹¹.
Earth's spin and shape reach the pull at the equator
IERS gives a mean equatorial gravity of 9.7803278 m s⁻². Newton's formula with Earth's GM and the 6,371 km textbook radius gives 9.82025, about 0.41% more; with the equatorial radius of 6,378,136.6 m it gives 9.79829, 0.18% more. The formula ignores Earth's rotation and shape.
Rotation alone, at IERS's nominal spin rate, takes 0.0339 m s⁻² off at the equator, nearly twice the 0.018 gap left with the equatorial radius. The equatorial bulge, through the J2 term IERS lists, adds back roughly 0.016. As shares of g, on our arithmetic, the bulge term is about 72 times G's relative uncertainty and the spin term about 154 times. The calculation never needed G: it runs on GM.
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