From the electron to the whole universe, everything that exists fits inside one triangle. Two of its edges are built from just three constants, G, ħ and c: squeeze anything past them and it either collapses into a black hole or dissolves into quantum blur.
Crush the whole Earth into a ball about 1.8 cm across, the size of a marble, and it becomes a black hole.
It would become a black hole if squeezed to a radius of 8.87 mm.
rs = 2GM/c² · 7.2 × 10⁸ times smaller than it is now
Source: NASA Planetary Fact Sheets
Click a dot for details · drag to pan · double-click to zoom
Enter a mass and a length. We plot half the length as the radius and tell you which side of the walls it lands on.
Left to right is mass in kilograms; bottom to top is size, as a radius in metres. Both axes are logarithmic: every power of ten gets the same space, so the chart spans 128 powers of ten in mass and 66 in size. Read the exponents on the axes to see how far apart two objects really are.
Straight lines mean simple laws. Where size grows in step with mass, the line rises with slope +1; where size shrinks as mass grows, it falls with slope −1; and every shallower line, with slope ⅓, is a constant density, because volume grows as the cube of the radius.
r = 2GM/c²
Pack a mass M inside its Schwarzschild radius and nothing, not even light, gets out. Nothing can be smaller than this for its mass, because it would already be a black hole. Black holes themselves sit right on the line.
r = ħ / (Mc)
Nothing can be pinned down more tightly than its reduced Compton wavelength: squeeze a particle into a smaller region and the energy needed starts creating new particles instead. Point particles such as the electron sit on this line.
r = c / H₀
The third edge is the Hubble radius c/H₀, about 1.4 × 10²⁶ m or 14.5 billion light-years: the distance at which the expansion of space carries galaxies away at the speed of light. It is the size scale of the universe today. (The observable universe is about three times larger, because light from beyond the Hubble radius can still reach us.)
The black-hole line and the quantum line cross at a mass of 1.54 × 10⁻⁸ kg and a radius of 2.29 × 10⁻³⁵ m, within a factor of √2 of the Planck mass (2.18 × 10⁻⁸ kg) and the Planck length (1.62 × 10⁻³⁵ m). Both are built from only three constants of nature: G, ħ and c. Below this point gravity and quantum mechanics both matter at once, and no tested theory says what happens there.
See G, ħ and c in the physics constants table →Atoms, raindrops, people, rocks and planets all lie close to the water-density line. Ordinary matter is atoms packed shoulder to shoulder, so it stays within a factor of ten or so of 1,000 kg/m³ from a molecule to a planet.
Atomic nuclei and neutron stars share a second line, about 10¹⁴ times denser. A neutron star is, in effect, one giant nucleus held together by gravity instead of the strong force.
Every point with its source. Size is the radius; for objects that are not round it is half the largest dimension, and for black holes it is the event-horizon radius. Density is shown only for roughly round objects.
| Object | Mass (kg) | Radius (m) | Mean density (kg/m³) | Source |
|---|---|---|---|---|
| Particles, nuclei & atoms | ||||
| Neutrino (upper limit) | < 8.02 × 10⁻³⁷ | > 4.39 × 10⁻⁷ | — | KATRIN Collaboration, Science 388, 180 (2025) — upper limit |
| Electron | 9.11 × 10⁻³¹ | 3.86 × 10⁻¹³ | — | CODATA 2022 (NIST) |
| Proton | 1.67 × 10⁻²⁷ | 8.41 × 10⁻¹⁶ | 6.72 × 10¹⁷ | CODATA 2022 (NIST) |
| Higgs boson | 2.23 × 10⁻²⁵ | 1.58 × 10⁻¹⁸ | — | Particle Data Group, Review of Particle Physics (2024) |
| Uranium nucleus | 3.95 × 10⁻²⁵ | 7.44 × 10⁻¹⁵ | 2.29 × 10¹⁷ | K. S. Krane, Introductory Nuclear Physics (R = 1.2 fm × A^1/3) |
| Hydrogen atom | 1.67 × 10⁻²⁷ | 5.29 × 10⁻¹¹ | 2.7 × 10³ | CODATA 2022 (NIST) |
| Caesium atom | 2.21 × 10⁻²⁵ | 2.6 × 10⁻¹⁰ | 3 × 10³ | J. C. Slater, J. Chem. Phys. 41, 3199 (1964) |
| Water molecule | 2.99 × 10⁻²⁶ | 1.4 × 10⁻¹⁰ | 2.6 × 10³ | Water: 18.015 u, ≈0.28 nm effective diameter; raindrop = 2 mm drop (1 mm radius) of water |
| Hemoglobin protein | 1.07 × 10⁻²² | 2.75 × 10⁻⁹ | 1.23 × 10³ | R. Milo & R. Phillips, Cell Biology by the Numbers (2015) |
| Life & everyday things | ||||
| Coronavirus (SARS-CoV-2) | 1 × 10⁻¹⁸ | 5 × 10⁻⁸ | 1.91 × 10³ | Bar-On et al., eLife 9, e57309 (2020) |
| E. coli bacterium | 1 × 10⁻¹⁵ | 1 × 10⁻⁶ | — | R. Milo & R. Phillips, Cell Biology by the Numbers (2015) |
| Red blood cell | 1 × 10⁻¹³ | 3.9 × 10⁻⁶ | — | R. Milo & R. Phillips, Cell Biology by the Numbers (2015) |
| Raindrop | 4.19 × 10⁻⁶ | 1 × 10⁻³ | 1 × 10³ | Water: 18.015 u, ≈0.28 nm effective diameter; raindrop = 2 mm drop (1 mm radius) of water |
| US penny | 2.5 × 10⁻³ | 9.53 × 10⁻³ | — | National mint specifications (mass and diameter) |
| Human | 73 | 0.88 | — | ICRP Publication 89, reference adult male (73 kg, 176 cm) |
| Blue whale | 1.5 × 10⁵ | 16.8 | — | NOAA Fisheries, Blue whale (up to 110 ft, 330,000 lb) |
| International Space Station | 4.2 × 10⁵ | 54.5 | — | NASA, International Space Station facts and figures |
| Great Pyramid of Giza | 6 × 10⁹ | 163 | — | M. Lehner, The Complete Pyramids (1997) — ≈6 million tonnes, 230 m base (radius = half the 326 m base diagonal) |
| Asteroids, moons & planets | ||||
| Asteroid Bennu | 7.33 × 10¹⁰ | 245 | 1.19 × 10³ | Lauretta et al., Nature 568, 55 (2019) — OSIRIS-REx |
| Dwarf planet Ceres | 9.38 × 10²⁰ | 4.7 × 10⁵ | 2.16 × 10³ | Park et al., Nature 537, 515 (2016) — Dawn |
| Moon | 7.35 × 10²² | 1.74 × 10⁶ | 3.34 × 10³ | NASA Planetary Fact Sheets |
| Earth | 5.97 × 10²⁴ | 6.37 × 10⁶ | 5.51 × 10³ | NASA Planetary Fact Sheets |
| Jupiter | 1.9 × 10²⁷ | 6.99 × 10⁷ | 1.33 × 10³ | NASA Planetary Fact Sheets |
| Stars & dead stars | ||||
| Sun | 1.99 × 10³⁰ | 6.96 × 10⁸ | 1.41 × 10³ | IAU 2015 Resolution B3 (nominal solar values) |
| Sirius A | 4.1 × 10³⁰ | 1.19 × 10⁹ | 581 | Bond et al., ApJ 840, 70 (2017); Kervella et al., A&A 408, 681 (2003) |
| Betelgeuse | 3.58 × 10³¹ | 5.32 × 10¹¹ | 5.69 × 10⁻⁵ | Joyce et al., ApJ 902, 63 (2020) |
| Sirius B (white dwarf) | 2.02 × 10³⁰ | 5.63 × 10⁶ | 2.7 × 10⁹ | Bond et al., ApJ 840, 70 (2017) — mass and radius |
| Neutron star | 4.14 × 10³⁰ | 1.24 × 10⁴ | 5.19 × 10¹⁷ | PSR J0740+6620: Riley et al., ApJL 918, L27 (2021) — radius; Fonseca et al., ApJL 915, L12 (2021) — mass |
| Black holes | ||||
| Cygnus X-1 black hole | 4.22 × 10³¹ | 6.26 × 10⁴ | — | Miller-Jones et al., Science 371, 1046 (2021) |
| Sagittarius A* | 8.54 × 10³⁶ | 1.27 × 10¹⁰ | — | GRAVITY Collaboration, A&A 657, L12 (2022) |
| M87* black hole | 1.29 × 10⁴⁰ | 1.92 × 10¹³ | — | Event Horizon Telescope Collaboration, ApJL 875, L6 (2019) |
| Galaxies & the universe | ||||
| Solar System (out to Neptune) | 1.99 × 10³⁰ | 4.5 × 10¹² | — | NASA Planetary Fact Sheets |
| Milky Way | 4.18 × 10⁴¹ | 6.48 × 10²⁰ | — | Watkins et al., ApJ 873, 118 (2019) — mass within 21 kpc |
| Galaxy cluster | 1.99 × 10⁴⁵ | 6.17 × 10²² | — | Kravtsov & Borgani, ARA&A 50, 353 (2012) — typical rich cluster |
| Universe (Hubble sphere) | 9.24 × 10⁵² | 1.37 × 10²⁶ | — | Planck Collaboration, A&A 641, A6 (2020) — H₀ = 67.4 km/s/Mpc |
Earth's Schwarzschild radius is 2GM/c² = 8.87 mm. To become a black hole, the whole planet would have to be crushed into a ball about 1.8 cm across, roughly the size of a marble.
Around the Planck mass, 2.18 × 10⁻⁸ kg, about the mass of a grain of sand. Anything lighter would have an event horizon smaller than its own quantum wavelength, where the idea of a black hole stops making sense. Every black hole observed so far is at least a few times the mass of the Sun.
The universe within the Hubble radius lands on the black-hole line because, for a flat universe at the critical density, c/H₀ equals 2GM/c² for the mass inside it. But a black hole is matter collapsing inside a larger space, while the universe is expanding and has no outside, so the comparison stops there.
Experiments have found no internal size for the electron, so it is plotted at its reduced Compton wavelength ħ/(mₑc) = 3.86 × 10⁻¹³ m. Below that scale it cannot be pinned down without the energy creating new particles.
It follows the mass–size diagram of Lineweaver and Patel, “All objects and some questions” (American Journal of Physics, 2023). Here the lines are computed from CODATA values of G, ħ and c and the Planck 2018 Hubble constant, and every object's mass and size are cited in the table.
The chart follows the mass–size diagram in C. H. Lineweaver & V. M. Patel, “All objects and some questions”, Am. J. Phys. 91, 819 (2023); erratum 92, 240 (2024)
Lines computed from G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2022), ħ = h/2π with h = 6.62607015 × 10⁻³⁴ J s (exact), c = 299,792,458 m/s (exact) and H₀ = 67.4 km/s/Mpc (Planck 2018).