Orders of magnitude (length)

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The following are examples of orders of magnitude for different lengths.

Section Range (m) Unit Example Items
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Planck area 10−35 fm Quantum foam
Subatomic 10−35 10−15 am electron, quark, string
Atomic and cellular 10−15 10−12 fm proton, neutron
10−12 10−9 pm wavelength of gamma rays and X-rays, hydrogen atom
10−9 10−6 nm DNA helix, virus, wavelength of optical spectrum
Human scale 10−6 10−3 µm bacterium, fog water droplet, human hair[1]
10−3 100 mm mosquito, golf ball, football
100 103 m human being, football field, Eiffel Tower
103 106 km Mount Everest, length of Panama Canal, larger asteroid
Astronomical 106 109 Mm the Moon, Earth, one light-second
109 1012 Gm Sun, one light-minute, Earth's orbit
1012 1015 Tm orbits of outer planets, Solar System
1015 1018 Pm one light-year; distance to Proxima Centauri
1018 1021 Em galactic arm
1021 1024 Zm Milky Way, distance to Andromeda Galaxy
1024 10^{10^{10^{122}}}[note 1] Ym Huge-LQG, Hercules-Corona Borealis Great Wall, visible universe

Detailed list[edit]

To help compare different orders of magnitude, the following list describes various lengths between 1.6×10−35 meters and 10^{10^{10^{122}}}meters.

Subatomic[edit]

Factor (m) Multiple Value Item
10−35 1 Planck Length 0.0000000000162 ym (1.62×10−35 m) Planck length; typical scale of hypothetical loop quantum gravity or size of a hypothetical string and of branes; according to string theory lengths smaller than this do not make any physical sense.[2] Quantum foam is thought to exist at this level.
10−24 1 yoctometre (ym) 20 ym (2 × 10−23 metres) effective cross section radius of 1 MeV neutrinos[3]
10−21 1 zeptometre (zm) Preons, hypothetical particles proposed as subcomponents of quarks and leptons; the upper bound for the width of a cosmic string in string theory.
7 zm (7 × 10−21 metres) effective cross section radius of high energy neutrinos[4]
310 zm (3.10 × 10−19 metres) de Broglie wavelength of protons at the Large Hadron Collider (4 TeV as of 2012)
10−18 1 attometre (am) upper limit for the size of quarks and electrons
sensitivity of the LIGO detector for gravitational waves
upper bound of the typical size range for "fundamental strings"[2]
10−17 10 am range of the weak force

Atomic and cellular[edit]

1 E-15m - Click on the relevant thumbnail image to jump to the desired order of length magnitude: left is 1e-15m, right is 1e-8m. Click on information icon bottom-left for description of image. 1 E-14 m 1 E-13 m 1 E-12 m 1 E-11 m 1 E-10 m 1 E-9 m 1 E-8 m 1 E-7 m
Clickable image. The thumbnails range left to right from 1e-15m to 1e-7m. (Image description)
Factor (m) Multiple Value Item
10−15 1 femtometre (fm) 1.5 fm size of an 11 MeV proton[5]
2.81794 fm classical electron radius[6]
scale of the atomic nucleus[2][7]
10−14 10 fm
10−13 100 fm
10−12 1 picometre (pm) ... longest wavelength of gamma rays
2.4 pm Compton wavelength of electron
5 pm wavelength of shortest X-rays
10−11 10 pm 25 pm radius of hydrogen atom
31 pm radius of helium atom
53 pm Bohr radius
10−10 100 pm 100 pm (0.1 nm) 1 Ångström (also covalent radius of sulfur atom[8])
154 pm (0.154 nm) length of a typical covalent bond (C–C).
500 pm (0.50 nm) width of protein α helix
10−9 1 nanometre (nm) 1 nm diameter of a carbon nanotube[9]
2.5 nm Smallest microprocessor transistor gate oxide thickness (as of Jan 2007)
6–10 nm thickness of cell membrane
10−8 10 nm 10 nm thickness of cell wall in gram-negative bacteria[citation needed]
40 nm extreme ultraviolet wavelength
90 nm Human immunodeficiency virus (HIV) (generally, viruses range in size from 20 nm to 450 nm)
10−7 100 nm 121.6 nm wavelength of the Lyman-alpha line[10]
380–435 nm wavelength of violet light—see color and optical spectrum[11]
625–740 nm wavelength of red light[11]

Human scale[edit]

1 E-6 m - Click on the relevant thumbnail image to jump to the desired order of length magnitude: top-left is 1e-6m, bottom-right is 1e5m. Click on information icon bottom-left for description of image. 1 E-5 m 1 E-4 m 1 E-3 m 1 E-2 m 1 E-1 m 1 E0 m 1 E1 m 1 E2 m 1 E3 m 1 E4 m 1 E5 m
Click on the thumbnail image to jump to the desired order of length magnitude article: top-left is 1E-6m (10−6), lower-right is 1E5m (105). (Image description)
Factor (m) Multiple Value Item
10−6 1 micrometre (µm) 1 µm also called one micron
1–3 µm particle size that a surgical mask removes at 80–95% efficiency[citation needed]
6-8 µm diameter of a red blood cell[12]
10−5 10 µm 10 µm typical size of a fog, mist or cloud water droplet. Chip 10 µm process in 1971.
12 µm width of acrylic fibre
25.4 µm 1/1000 inch, commonly referred to as one thou or one mil
10−4 100 µm 100 µm average width of a strand of human hair[1]
200 µm typical length of Paramecium caudatum, a ciliate protist
750 µm maximum diameter of Thiomargarita namibiensis, the largest bacterium ever discovered
10−3 1 millimetre (mm) 2.54 mm 1/10th inch; distance between pins in DIP (dual-inline-package) electronic components
5 mm length of average red ant
7.62 mm common military ammunition size
10−2 1 centimetre (cm) 1.5 cm length of a large mosquito
2.54 cm 1 inch
4.267 cm diameter of a golf ball
10−1 1 decimetre (dm) 10 cm wavelength of the highest UHF radio frequency, 3 GHz
30.48 cm 1 foot
91.44 cm 1 yard
100 1 metre 1 m wavelength of the lowest UHF and highest VHF radio frequency, 300 MHz
1.7 m (5 feet 7 inches) average height of a human
8.38 m The length of a London Bus (Routemaster)
101 1 decametre (dam) 10 m wavelength of the lowest VHF and highest shortwave radio frequency, 30 MHz
33 m length of longest blue whale measured, the largest animal[13]
93.47 m height of the Statue of Liberty (foundation of pedestal to torch)
102 1 hectometre (hm) 100 m wavelength of the lowest shortwave radio frequency and highest medium wave radio frequency, 3 MHz
137 m (147 m) height (present and original) of the Great Pyramid of Giza
979 m height of the Salto Angel, the world's highest free-falling waterfall (Venezuela)
103 1 kilometre (km) 1 km wavelength of the lowest medium wave radio frequency, 300 kHz
1609 m 1 international mile
1852 m 1 nautical mile
 
8848 m height of the highest mountain on earth, Mount Everest
104 10 km 10.911 km depth of deepest part of the ocean, Mariana Trench
13 km narrowest width of the Strait of Gibraltar, separating Europe and Africa
90 km width of the Bering Strait
105 100 km 111 km distance covered by one degree of latitude on Earth's surface
163 km length of the Suez Canal
974.6 km greatest diameter[14] of the dwarf planet[note 2] Ceres

Astronomical[edit]

An illustration of the sizes of planets and stars
1 E6 m - Click on the relevant thumbnail image to jump to the desired order of length magnitude: left is 1e6m, right is 1e13m. Click on information icon bottom-left for description of image. 1 E7 m 1 E8 m 1 E9 m 1 E10 m 1 E11 m 1 E12 m 1 E13 m 1 E14 m 1 E15 m 1 E16 m 1 E17 m
Click on the thumbnail image to jump to the desired order of length magnitude: top-left is 1e6m, lower-right is 1e17m. (Image description)
Factor (m) Multiple Value Item
106 1,000 km = 1 megametre (Mm) 2,390 km diameter of dwarf planet Pluto, formerly the smallest planet category[note 2] of our solar system
3,480 km diameter of the Moon
5,200 km typical distance covered by the winner of the 24 Hours of Le Mans automobile endurance race
6,400 km length of the Great Wall of China
6,600 km approximate length of the two longest rivers, the Nile and the Amazon
7,821 km length of the Trans-Canada Highway
9,288 km length of the Trans-Siberian Railway, longest in the world
107 10,000 km 12,756 km equatorial diameter of the Earth
40,075 km length of the Earth's equator
108 100,000 km 142,984 km diameter of Jupiter
299,792.458 km distance travelled by light in one second
384,000 km = 384 Mm Moon's orbital distance from Earth
109 1 million km = 1 gigametre (Gm) 1,390,000 km = 1.39 Gm diameter of the Sun
4,200,000  km = 4.2 Gm greatest mileage ever recorded by a car (A 1966 Volvo P-1800S, still driving)
1010 10 million km 18 million km approximately one light-minute
1011 100 million km 150 million km = 150 Gm 1 astronomical unit (AU); mean distance between Earth and Sun
~ 900 Gm optical diameter of Betelgeuse (~600 × Sun)
1012 1000 million km = 1 terametre (Tm) 1.4 ×109 km orbital distance of Saturn from Sun
1.96 ×109 km estimated optical diameter of VY Canis Majoris (1420 × Sun)
2.3 ×109 km estimated optical diameter of NML Cygni (1650 × Sun)
2.37 ×109 km median point of the optical diameter of UY Scuti, as of 2014 the largest known star
5.9 ×109 km = 5.9 Tm orbital distance of Pluto from Sun
~ 7.5 ×109 km = 7.5 Tm outer boundary of the Kuiper belt, inner boundary of the Oort cloud (~ 50 AU)
1013 10 Tm diameter of our Solar System as a whole[2]
16.25×109 km = 16.25 Tm distance of the Voyager 1 spacecraft from Sun (as of Feb 2009), the farthest man-made object so far[15]
62.03×109 km = 62.03 Tm estimated radius of the event horizon of the supermassive black hole in NGC 4889, the largest known black hole to date
1014 100 Tm 1.8×1011 km = 180 Tm size of the debris disk around the star 51 Pegasi [16]
1015 1 petametre (Pm) ~ 7.5 ×1012 km = 7.5 Pm supposed outer boundary of the Oort cloud (~ 50,000 AU)
9.46×1012 km = 9.46 Pm
= 1 light year
distance travelled by light in one year; at its current speed, Voyager 1 would need 17,500 years to travel this distance
1016 10 Pm 3.2616 light-years
(3.0857×1013 km = 30.857 Pm)
1 parsec
4.22 light-years = 39.9 Pm distance to nearest star (Proxima Centauri)
4.37 light-years = 41.3 Pm as of March 2013, distance to nearest discovered extrasolar planet (Alpha Centauri Bb)
1017 100 Pm 20.4 light-years = 193 Pm as of October 2010, distance to nearest discovered extrasolar planet with potential to support life as we know it (Gliese 581 d)
65 light-years = 6.15×1017 m = 615 Pm approximate radius of humanity's radio bubble, caused by high-power TV broadcasts leaking through the atmosphere into outer space
1018 1 exametre (Em) 200 light-years = 1.9 Em distance to nearby solar twin (HIP 56948), a star with properties virtually identical to our Sun [17]
1019 10 Em 1,000 light-years = 9.46 Em or 9.46 × 1015 km average thickness of Milky Way Galaxy[18] (1000 to 3000 ly by 21 cm observations[19])
1020 100 Em 12,000 light-years = 113.5 Em or 1.135 × 1017 km thickness of Milky Way Galaxy's gaseous disk[20]
950 Em 100,000 light-years diameter of galactic disk of Milky Way Galaxy[2]
1021 1 zettametre (Zm)
50 kiloparsecs distance to SN 1987A, the most recent naked eye supernova
52 kiloparsecs = 1.62×1021 m = 1.62 Zm distance to the Large Magellanic Cloud (a dwarf galaxy orbiting the Milky Way)
54 kiloparsecs = 1.66 Zm distance to the Small Magellanic Cloud (another dwarf galaxy orbiting the Milky Way)
200 kiloparsecs = 6.15 Zm diameter of the low surface brightness disc halo of the giant spiral galaxy Malin 1
1022 10 Zm 13.25 Zm = 1.4 million light years
= 600 kiloparsecs
radius of the diffuse stellar halo of IC 1101, one of the largest known galaxies
24 Zm = 2.5 million light-years
= 770 kiloparsecs
distance to Andromeda Galaxy
3.26 million light-years
=30.8 Zm = 1 megaparsec
1 megaparsec
50 Zm (1.6 Mpc) diameter of Local Group of galaxies
1023 100 Zm 300–600 Zm = 10–20 megaparsecs distance to Virgo cluster of galaxies
1024 1 yottametre (Ym) 200 million light-years
= 1.9 Ym = 61 megaparsecs
diameter of the Local Supercluster and the largest voids and filaments.
300 million light-years
= 2.8 Ym = 100 megaparsecs
End of Greatness
550 million light-years
~170 megaparsecs ~5 Ym
diameter of the enormous Horologium Supercluster [21]
1 billion light-years
= 9.46 Ym =306 megaparsecs
diameter of the Pisces–Cetus Supercluster Complex, the supercluster complex where we live.
1025 10 Ym 1.37 billion light years
= 1.3×1025 m = 13 Ym
Length of the Sloan Great Wall, a giant wall of galaxies (galactic filament).[22]
3.26 billion light years
=30.8 Ym = 1 gigaparsec
1 gigaparsec
4 billion light years
=37.84 Ym
Length of the Huge-LQG, a group of 73 quasars
1026 100 Ym 1×1010 light-years
= 9.5×1025 m = 95 Ym
estimated light travel distance to certain quasars

length of the Hercules-Corona Borealis Great Wall, a colossal wall of galaxies, the largest and the most massive structure in the observable universe as of 2014

13.42 billion light years
=1.27×1026 m = 127 Ym
Estimated light travel distance to UDFj-39546284, the most distant object ever observed
9.2×1010 light years
= 8.7×1026 m = 870 Ym
approx. diameter (comoving distance) of the visible universe[2]
1027 1000 Ym ~250 billion light years
= 2.4×1027 m = 2400 Ym
lower bound of the (possibly infinite) radius of the universe, if it is a 3-sphere, according to one estimate using the WMAP data at 95% confidence.[23] It equivalently implies that there are at minimum 21 particle horizon-sized volumes in the universe.
~400 billion light years
= 3.8×1027 m = 3800 Ym
Lower bound of the homogeneous universe derived from the Planck spacecraft [24]
10^{10^{115}}[note 1] 10^{10^{115}} Ym 10^{10^{115}} megaparsecs
= 10^{10^{115}} m
= 10^{10^{115}}Ym
According to the laws of probability, the distance one must travel until one encounters a volume of space identical to our observable universe with conditions identical to our own.[25][26]
10^{10^{10^{122}}}[note 1] 10^{10^{10^{122}}} Ym 10^{10^{10^{122}}} Mpc
= 10^{10^{10^{122}}} m
= 10^{10^{10^{122}}}Ym
size of universe after cosmological inflation, implied by one resolution of the No-Boundary Proposal[27]

See also[edit]

Notes[edit]

  1. ^ a b c 10115 is 1 followed by 115 zeroes, or a googol multiplied by a quadrillion. 1010115 is 1 followed by a quadrillion googol zeroes. 101010122is 1 followed by 1010122 (a googolplex10 sextillion) zeroes. These numbers are so vast that they are essentially the same in whatever units we could use to list them.
  2. ^ a b The exact category (asteroid, dwarf planet or planet) to which particular solar system objects belong, has been subject to some revision since the discovery of extrasolar planets and trans-Neptunian objects

References[edit]

  1. ^ a b According to The Physics Factbook, the diameter of human hair ranges from 17 to 181 µm. Ley, Brian (1999). "Width of a Human Hair". The Physics Factbook. 
  2. ^ a b c d e f Cliff Burgess; Fernando Quevedo (November 2007). "The Great Cosmic Roller-Coaster Ride". Scientific American (print) (Scientific American, Inc.). p. 55. 
  3. ^ Carl R. Nave. "Cowan and Reines Neutrino Experiment". Retrieved 2008-12-04.  (6.3 × 10−44 cm2, which gives an effective radius of about 2 × 10−23 m)
  4. ^ Carl R. Nave. "Neutron Absorption Cross-sections". Retrieved 2008-12-04.  (area for 20 GeV about 10 × 10−42 m2 gives effective radius of about 2 × 10−21 m; for 250 GeV about 150 × 10−42 m2 gives effective radius of about 7 × 10−21 m)
  5. ^ Carl R. Nave. "Scattering Cross Section". Retrieved 2009-02-10.  (diameter of the Scattering Cross Section of an 11 MeV proton with a target proton)
  6. ^ NIST. CODATA Value: classical electron radius. Retrieved 2009-02-10
  7. ^ H. E. Smith. "The Scale of the Universe". UCSD. Retrieved 2009-02-10. "~10-13cm" 
  8. ^ Mark Winter (2008). "WebElements Periodic Table of the Elements / Sulfur / Radii". Retrieved 2008-12-06. 
  9. ^ Flahaut, E.; Bacsa R, Peigney A, Laurent C. (2003). "Gram-Scale CCVD Synthesis of Double-Walled Carbon Nanotubes". Chemical Communications 12 (12): 1442–1443. doi:10.1039/b301514a. PMID 12841282. Retrieved 2008-11-14. 
  10. ^ Cohn, J. University of California, Berkeley Lyman alpha systems and cosmology. Retrieved 2009-02-21
  11. ^ a b Color
  12. ^ "Through the Microscope: Blood Cells - Life's Blood". Wadsworth Center, New York State Department of Health. Retrieved 2011-09-13. 
  13. ^ "Animal Records". Smithsonian National Zoological Park. Retrieved 2007-05-29. 
  14. ^ Thomas, P. C.; Parker, J. Wm.; McFadden, L. A.; et al. (2005). "Differentiation of the asteroid Ceres as revealed by its shape". Nature 437 (7056): 224–226. Bibcode:2005Natur.437..224T. doi:10.1038/nature03938. PMID 16148926. 
  15. ^ Spacecraft escaping the Solar System
  16. ^ Twin Keck telescopes probe dual dust disks
  17. ^ Shiga, David. "Sun's 'twin' an ideal hunting ground for alien life". New Scientist. Retrieved 2007-10-03. 
  18. ^ Christian, Eric; Samar, Safi-Harb. "How large is the Milky Way?". Retrieved 2008-11-14. 
  19. ^ Duncan, Martin (2008). "16". Physics 216 – Introduction to Astrophysics. Retrieved 2008-11-14. 
  20. ^ "Milky Way fatter than first thought". The Sydney Morning Herald. Australian Associated Press. 2008-02-20. Retrieved 2008-11-14. 
  21. ^ http://www.atlasoftheuniverse.com/superc/hor.html The Horologium Supercluster
  22. ^ J. R. Gott III et al., Astrophys. J., 624, 463 (2005). Figure 8 – "Logarithmic Maps of the Universe" – is available as a poster from the homepage of Mario Juric.
  23. ^ http://arxiv.org/abs/astro-ph/0605709v2 How Many Universes Do There Need To Be?
  24. ^ data
  25. ^ "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark M., Sci Am. 2003 May;288(5):40-51.
  26. ^ Max Tegmark (2003). "Parallel Universes". In "Science and Ultimate Reality: from Quantum to Cosmos", honoring John Wheeler's 90th birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper eds. Cambridge University Press (2003). arXiv:astro-ph/0302131. Bibcode:2003astro.ph..2131T. 
  27. ^ http://arxiv.org/abs/hep-th/0610199 "Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions "

External links[edit]